Is it a factor haveI dreamt itthat, by means of electricity, theworld of matter has becomeagreat nerve, vibrating thousands of miles in a breathless point of time? Rather, theround globeis a vast head, a brain, instinct with intelligence! Or, shall wesay, it is itself a thought, nothingbut thought, and no longer thesubstancethat wedreamed it? Nathaniel HawthorneTheHouseOf Seven Gables 1851ProloguePOWER SYSTEM ECONOMICS PROVIDES A PRACTICAL INTRODUC- TION TO POWER-MARKET DESIGN. To assist engineers, lawyers, regulators,and economists in crossing the boundaries between their fields, it provides thenecessary background in economics and engineering. While Part 1 covers basics,it provides fresh insights ranging from a streamlined method for calculations, tothe adaptation of economics to the quirks of generation models, to the distinctionbetween the market structure and market architecture.Part2 focuses on the core structure of power markets which determines the basiccharacter of supply and demand. It encompasses demand-side flaws, short-runreliability policy and the rigidities of supply. Together these determine the notoriousprice-spikes and unstable investment pattern of power markets. Because of itsfundamental nature, this analysis can proceed without reference to locational pricingor unit commitment which gives less-technical readers access to the most importantand fundamental economics of power markets.Part3 discusses the architecture of the day-ahead and real-time markets. Thisrequires the introduction and analysis of the unit-commitment problemtheproblem of starting and stopping generators economically. To avoid unnecessarycomplexity, the other primary problem of power-system economics, networkcongestion, is postponed until Part 5. This allows a clearer comparison of the threefundamental types of power trading: bilateral trading, exchange trading and pool-based trading. Part4 detours from the drive toward an increasingly detailed view of the marketto examine market power. Although best understood in the context of Parts2 andFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. See Platt (1991) for information on central station companies and Samuel Insull. The quotation (p. 86)is froma contemporary account of Insulls address. Platt describes early competition as follows: TheChicago experience of rate wars, distributor duplication, and torn-up streets presented an alternative thatwas attractive to virtually no one. For state commissions and progressives, see Rudolph & Ridley (1986).2. Smith (1995) relies on Gregg J arrell to conclude regulation was a response to the utilities' desire toprotect profits, not a consumerist response to monopoly pricing. But Knittel (1999) tests causation byutilities and consumers and finds no significant correlation between profit change and regulation aftercorrecting J arrells endogeneity problem. This result would be expected froman analysis of profit whentwo equal forces have opposite motivations with respect to its level.Thepropensity to truck, barter, and exchangeonething for another . . . is common to all men.Adam SmithTheWealth of Nations1776Chapter 1-1Why Deregulate?IN THE BEGINNING THERE WAS COMPETITIONBRUTAL AND INEFFI-CIENT. Between 1887 and 1893, twenty-four central station power companieswere established within Chicago alone. With overlapping distribution lines, competi-tion for customers was fierce and costs were high. In 1898, the same year he waselected president of the National Electric Light Association, Samuel Insull solvedthese problems by acquiring a monopoly over all central-station production inChicago. In his historic presidential address to NELA, Insull explained not onlywhy the electricity business was a natural monopoly but why it should be regu-lated and why this regulation should be at the state level, not the local level. Insullargued thatexclusive franchises should be coupled with the conditions ofpublic control, requiring all charges for services fixed by publicbodies to be based on cost plus a reasonable profit.These ideas shocked his fellow utility executives but led fairly directly to regulatorylaws passed by New York and Wisconsin in 1907 establishing the first two stateutility commissions. Reformers of the Progressive era also lent support to regulationalthough they were about equally supportive of municipal power companies.1 Theirintention, to hold down monopoly profits, was at odds with Insulls desire to keepprofits above the competitive level, but both sides agreed that competition wasinefficient and that providing electricity was a natural monopoly.2February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Nothing is moreterriblethan activity without insight.Thomas Carlyle(1795-1881)Chapter 1-2What to DeregulateDELIVERED POWER IS A BUNDLE OF MANY SERVICES. These includetransmission, distribution, frequency control, and voltage support, as well asgeneration. The first two deliver the power while the second two maintain powerquality; other services provide reliability.Each service requires a separate market, and some require several markets. Thisraises many questions about which services should be deregulated and which shouldnot. Even within a market for a single service, one sideeither demand orsupplymay need to be regulated while the other side of the market can be deregu-lated. For instance, the supply of transmission rights must be determined by thesystem operator, but the demand side of this market is competitive. In contrast,the demands for ancillary services are determined by the system operator whilethe supply sides of these markets can be competitive. The most critical service in a regulated or a deregulated power market is thatprovided by the system operator. This is a coordination service. For a deregulatedmarket it typically includes operation of the real-time markets and a day-aheadmarket. These provide scheduling and balancing services, but operating thesemarkets is itself an entirely separate service. While the need for the systemoperatorservice is agreed to by all, the proper extent of that service is the subject of thecentral controversy in power market design.Chapter Summary 1-2: Many services are required to bring high-quality reliablepower to end users. Each might be provided by free markets, by the state, byregulated suppliers, or by some hybrid arrangement. Bulk power generation is thesource of nearly half the cost of retail power and is one of the services most easilyprovided by a competitive market. Moreover, it seems to offer several possibilitiesFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. In Tables 14 through 17 of one such report (DOE 1998a) the useful (amortized) fixed costs are notreported, and the fixed O&M costs are reported in $/kW which may be an amortized value reported withthe wrong units or, if the units are correct, may represent a misguided conversion of an amortized cost toan overnight cost.It is not too much to expect that our children will enjoy in their homeselectricity too cheap to meter.Lewis L. StraussChairman, Atomic Energy Commission1954Chapter 1-3Pricing Power, Energy, and CapacityPOWER IS THE RATE OF FLOW OF ENERGY. Similarly, generating capacity,the ability to produce power is itself a flow. A megawatt (MW) of capacity is worthlittle if it lasts only a minute just as a MW of power delivered for only a minuteis worth little. But a MW of power or capacity that flows for a year is quite valuable.The price of both power and energy can be measured in $/MWh, and sincecapacity is a flow like power and measured in MW, like power, it is priced likepower, in $/MWh. Many find this confusing, but an examination of screening curvesshows that this is traditional (as well as necessary). Since fixed costs are mainlythe cost of capacity they are measured in $/MWh and can be added to variable coststo find total cost in $/MWh.When generation cost data are presented, capacity cost is usually stated in $/kW.This is the cost of the flow of capacity produced by a generator over its lifetime,so the true (but unstated) units are $/kW-lifetime. This cost provides useful informa-tion but only for the purpose of finding fixed costs that can be expressed in $/MWh.No other useful economic computation can be performed with the overnight costof capacity given in $/kW because they cannot be compared with other costs untillevelized. While the U.S. Department of Energy sometimes computes theseeconomically useful (levelized) fixed costs, it never publishes them. Instead itcombines them with variable costs and reports total levelized energy costs.1 Thisis the result of a widespread lack of understanding of the nature of capacity costs.Confusion over units causes too many different units to be used, and this requiresunnecessary and sometimes impossible conversions. This chapter shows how tomake almost all relevant economic calculations by expressing almost all prices andFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.And when theRain has wet theKiteand Twine, so that it can conduct theElectric Firefreely,you will find it stream out plentifully from theKey on theApproach of your Knuckle.Benjamin Franklin1752Chapter 1-4Power Supply and DemandTHE PHYSICAL ASPECTS OF SUPPLY AND DEMAND PLAY A PROMINENTROLE IN POWER MARKETS. Shifts in demand, not associated with price, playa role in all markets, but in power markets they often receive attention to theexclusion of price. This is not simply the result of regulatory pricing; even withmarket prices, demand shifts will play a key role in determining the mix of produc-tion technologies. In this way hourly demand fluctuations determine key long-runcharacteristics of supply.Because electric power cannot be stored, production always equals consumption,so the difference between supply and demand cannot be indicated by flows ofpower. Neither is the instantaneous difference indicated by contracts since real-timedemand is determined by customers physically taking power. The short-runsupplydemand balance is indicated by voltage and, especially, frequency. Thisunusual market structure requires some elementary background in system physics.More detail is provided in Chapters 5-1 and 5-2.Chapter Summary 1-4: Load duration curves are still relevant in unregulatedmarkets, but their role in analysis is more subtle because their shape is affectedby price and its correlation with load. They can still be used with screening curvesto check an equilibrium, but to predict an equilibrium they must be used in combina-tion with price elasticity.Power production always equals consumption (counting losses as part ofconsumption) which makes it impossible to assess the supplydemand balance byobserving quantities or quantity flows. Instead, frequency is the proper indicatorof system-wide balance, and net unscheduled flows between regions are used toshare the responsibility of maintaining this balance.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Therich, . . . in spiteof their natural selfishness and rapacity, . . . though thesoleend which theypropose. . . bethegratification of their own vain and insatiabledesires, they dividewith thepoortheproduceof all their improvements. They areled by an invisiblehand to makenearly thesamedistribution of thenecessaries of life, which would havebeen made, had theearth been dividedinto equal portions among all its inhabitants, and thus without intending it, without knowingit, advancetheinterest of thesociety.Adam SmithTheTheory of Moral Sentiments1759Chapter 1-5What Is Competition?COMPETITION IS LEAST POPULAR WITH THE COMPETITORS. Everysupplier wants to raise the market price, just as every buyer wants to lower it.Perfect competition frustrates both intentions.Some commodity markets provide almost perfect competition; eventually powermarkets may work almost as well. But designing such markets is difficult. Economiccompetition is not like competition in sports, which may be considered perfect whenthere are just two powerful and equal competitors. Economists consider competitionto be perfect when every competitor is small enough (atomistic is the term used)to have no discernable influence against the invisible hand of the market.Adam Smith guessed intuitively that a perfectly competitive market, in theeconomic sense, would produce an outcome that is in some way ideal. Manydifficulties can cause a market to fall short of this ideal, but even a market that isonly workably competitive can provide a powerful force for efficiency andinnovation.Power markets should be designed to be as competitive as possible but thatrequires an understanding of how competition works and what interferes with it.On its surface, competition is a simple process driven, as Adam Smith noted, byselfishness and rapacity; but the invisible hand works in subtle ways that are oftenmisunderstood. Those unfamiliar with these subtleties often conclude that suppliersare either going broke or making a fortune. This chapter explains the mechanismsthat keep supply and demand in balance while coordinating production and con-sumption to produce the promised efficient outcome.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Thetroublewith theworld is not that peopleknow too little,but that they know so many things that ain't so.Mark Twain(18351910)Chapter 1-6Marginal Cost in a Power MarketSIMPLIFIED DIAGRAMS OF GENERATION SUPPLY CURVES HAVE CON-FUSED THE DISCUSSION OF MARGINAL COST. Typically, these supply curvesare diagrammed to show a constant marginal cost up to the point of maximumgeneration. Then marginal cost becomes infinite without taking on intermediatevalues. Typically it jumps from about $30 to infinity with only an infinitesimalincrease in output. Mathematics calls such a jump a discontinuity. In fact, the curvewould be discontinuous if it jumped only from $30 to $40.The definition of marginal cost does not apply only to the points of discontinuity.Hence it does not apply to a right-angle supply curve at the point of full output,neither does it apply to the points of a market supply curve at which it jumps fromone generators marginal cost to the next. Unfortunately market equilibria sometimesoccur at such points, and concerns over market power often focus on them. Attemptsto apply the standard definition at these points can produce confusing and erroneousresults. Fortunately, the definition is based on mathematics that generalizes naturallyto discontinuous curves. Applying this generalization to the textbook definitionclears up the confusion and restores the economic results that otherwise appearto fail in power markets. For example, in power markets, as in all other markets,the competitive price is never greater than the marginal cost of production.Chapter Summary 1-6: Individual supply curves are often constructed withan abrupt end that causes the market supply curve to have abrupt steps. The standardmarginal-cost definition does not apply at such points. Instead, left- and right-handmarginal costs should be used to define the marginal-cost range. Then the competi-tive price, which remains well defined, will always lie within that range. A marketprice exceeding the marginal-cost range indicates market power.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Thework I haveset beforemeis this . . . how to get rid of theevils of competition whileretainingits advantages.Alfred Marshall(1842-1924)Chapter 1-7Market StructurePOOR MARKET STRUCTURE POSES THE GREATEST THREAT TO THEHEALTH OF POWER MARKETS. Structure refers to properties of the marketclosely tied to technology and ownership. The classic structural measure is aconcentration index for the ownership of production capacity. The cost structureof an industry, another component of market structure, describes both the costsof generation and the costs of transmission.Most aspects of market structure are difficult to alter and some, such as the highfixed costs of coal-fired generation, are impossible. But power markets containsome unusual technology-based arrangements that can easily be altered or thatrequire administrative decisions regarding their operation. These arrangements arepart of the market structure and require design just as do the architectural compo-nents described in the next chapter.The notion of market structure developed as part of the structure-conduct-performance paradigm of industrial organization in the early 1950s. The presentdiscussion, however, is based on the structure-architecture-rules classification ofmarket-design problems presented by Chao and Wilson (1999a) and Wilson (1999).The present chapter extends their definition of structure, particularly in the directionof administered reliability policies.Chapter Summary 1-7: Market structure has a decisive impact on market powerand investment. The second demand-side flaw, the ability of users to take powerfrom the grid in real time without a contract (see Section 1-1.5), makes structuralintervention necessary. Regulators must trade-off price spikes against involuntaryload shedding, thereby largely determining the incentives for investment in genera-tion capacity.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. This chapter owes a great debt to Wilson (1999) and Chao and Wilson (1999a), though it is notintended as a summary of their views.Thewholeworld may belooked upon as a vast general market madeup of diversespecial marketswhere social wealth is bought and sold. Our task then is to discover thelaws to which thesepurchases and sales tend to conform automatically. To this end, weshall supposethat themarketis perfectly competitive, just as in puremechanics wesuppose, to start with, that machines areperfectly frictionless.Leon Walras Elements of PureEconomics1874Chapter 1-8Market ArchitectureA MARKETS ARCHITECTURE IS A MAP OF ITS COMPONENTSUBMARKETS. This map includes the type of each market and the linkagesbetween them.1 The submarkets of a power market include the wholesale spotmarket, wholesale forward markets, and markets for ancillary services. Markettype classifies markets as, for example, bilateral, private exchange, or pool.Linkages between submarkets may be implicit price relationships caused byarbitrage or explicit rules linking rights purchased in one market to activity inanother.Architecture should be specified before rules are written, but it is often necessaryto test the architecture during the design process, and this requires a rough specifica-tion of the rules. Architectural design must also consider the market structure inwhich it is embedded, which may inhibit the proper function of some designs.Market design should not be rigidly compartmentalized, yet it is useful to considerthe markets architecture apart from the details of the rules and the limitations ofmarket structure.Chapter Summary 1-8: A market design or analysis project concerns a collec-tion of submarkets which are collectively referred to as the entire market. (Bothwill often be referred to simply as markets.) Deciding which submarkets shouldbe created for a power market is the first step in architectural design. Section 1-8.1briefly discusses day-ahead and real-time energy markets and transmission-rightsmarkets as a prelude to Part 3 which examines these choices in more depth.Private submarkets range from disorganized to highly centralized, and each hasits advantages. There is no simple rule for choosing between types of submarketsFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. One of several design flaws that produced this outcome was prohibiting the California ISO fromsubstituting a cheaper better product for a more expensive poorer product (Wolak, 1999). Also see Brien(1999).Genius is oneper cent inspiration, ninety-nineper cent perspiration.Thomas Edisonc. 1903If Edison had a needleto find in a haystack hewould proceed . . . to examinestraw after straw.A littletheory and calculation would havesaved him ninety percent of his labor.Nikola TeslaNew York Times1931Chapter 1-9Designing and Testing Market RulesUNTESTED MARKET DESIGNS CAUSE REAL-WORLD MARKET FAIL-URES. Suppliers are quick to take advantage of design flaws, especially those thatpay $9,999/MWh for a product that is worth less than $5/MWh.1 Currently, manyif not most, market designs are implemented without any explicit testing.Although the most serious market flaws typically arise fromstructural problems,while architectural problems rank second in importance, problems with rules arethe most numerous and their cost can be impressive. The design of rules is moreart than science, but economics offers two guiding principles: mimic the outcomeof a classically competitive market, and design markets so competitors find itprofitable to bid honestly. Simplicity is another virtue well worth pursuing butnotoriously difficult to define.Chapter Summary 1-9: In a pay-as-bid auction, a coal plant bidding its variablecost of $12/MWh would be paid $12/MWh, while in a single-price auction it wouldbe paid the system marginal cost which might be $100/MWh. In this case manywould object to paying the $100 competitive price to the inexpensive coal plantand seek to improve on the competitive model. Pay-as-bid is one suggestion. Theresult is gaming and, probably, a very modest decrease in price and a modestdecrease in efficiency. Ironically, if pay-as-bid succeeded as its advocates hope,it would put an end to investment in baseload and midload plants. In the long runthis would dramatically raise the cost of power. The pay-as-bid fallacy illustratesthe topics of the first three sections: the danger in attempting to subvert competition,the benefits of incentive compatible design, and the relevance of auction theory.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.When, by building theories upon theories, conclusions arederived which ceaseto beintelligible,it appears timeto search into thefoundations of thestructureand to investigatehow far thefactsreally warrant theconclusions.Charles Proteus SteinmetzThe Education of Electrical Engineers1902Chapter 2-1Reliability and Investment PolicyRELIABILITY, PRICE SPIKES, AND INVESTMENT ARE DETERMINED BYREGULATORY POLICIES. Because these policies impinge on market structurerather than architecture, they have been overlooked too often as debates focusedon nodal pricing, bilateral trading, or on market rules. The result has been achaotic pricing policy and disaster in the Western U.S. markets. Part 2 assumesaway two major problems, market power and transmission constraints, to focusexclusively on the structural core of a contemporary power market. The goal ofPart 2 is to explain the major policy options and their implications. This requiresan understanding of the causal links between policy controls and the key marketoutcomesreliability, price spikes and investment. Both controls and outcomesare diagrammed in Figure 2-1.1.Supply and demand characteristics comprise a markets core structure, but ina power market these are unusually complex. The supply side cannot store its outputso real-time production characteristics are important, and two demand-side flawsinteract detrimentally with this characteristic. Consequently, the market cannotoperate satisfactorily on its own. It requires a regulatory demand for a combinationof real-time energy, operating reserves, and installed capacity, and this demandmust be backed by a regulatory pricing policy. Without this reliability policy, thepower system would under-invest in generation because of the demand-side flaws.Reliability policy is the part of the structural core that can be affected immediatelyby design. The demand-side flaws can also be affected by policy, but these designchanges take longer to implement.Without the demand-side flaws and reliability policy, Figure 2-1.1 wouldrepresent a normal market; demand and supply conditions would feed into themarket and determine prices. These would determine new investment which wouldFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. Power markets are termed competitive if their supply side is competitive even when demand-sideflaws prevent the market fromdetermining competitive prices.Indebtedness to oxygenThechemist may repayBut not theobligationTo electricity.Emily Dickinson(183086)The Farthest Thunder That I HeardChapter 2-2Price Spikes Recover Fixed CostsWHAT PRICES WILL COVER A GENERATORS FIXED COSTS WITHOUTOVERCHARGING CONSUMERS? Short-run competitive prices perform thisservice and, in addition, induce the right level of investment in every type ofgeneration technology. This does not solve the long-run problems of power marketsbecause demand-side flaws prevent contemporary markets from determiningcompetitive prices.1 Subsequent chapters will discuss regulatory policies thatcompensate for these flaws, while this chapter focuses on how competitive powermarkets will work once the flaws are eliminated.Although not completely accurate, competitive analysis is useful for dispellingtwo fallacies concerning fixed costs. The first asserts that prices equal to marginalcost (competitive prices) cannot cover fixed costs. The second asserts that althoughthey can, they will do so only when the market is seriously short of capacity.Chapter Summary 2-2: Short-run competitive prices would recover fixed costsfor peakers and baseload plants alike. They would stimulate investment in the mixof technologies that produces the required power at least cost. Demand will occa-sionally push prices well above the average marginal cost of any supplier but notabove the right-hand marginal cost. These price spikes can be summarized witha price-duration curve that facilitates computation of the competitive outcome.Section 1: The Fixed-Cost Fallacy. This fallacy asserts that short-run competi-tive prices (marginal-cost prices) will prevent generators fromrecovering their fixedcosts. These are covered not because short-run competitive forces set price equalto marginal cost, but because, if they were not covered, investors would stopbuilding plants while demand continued to grow. This would cause shortages andFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. Both distribution and transmission outages typically cause more loss of load.Edison's design was a brilliant adaptation of thesimpleelectrical circuit: theelectric companysends electricity through a wireto a customer, then immediately gets theelectricity back throughanother wire, then (this is thebrilliant part) sends it right back to thecustomer again. Dave BarryChapter 2-3Reliability and GenerationRELIABILITY IS AT THE HEART OF EVERY DEBATE ABOUT ENERGYPRICE SPIKES. If these are large enough, they induce the investment that providesthe generating capacity necessary for a reliable system. In some markets capacityrequirements also play an important role. A shortage of installed generating capacityis not the only cause of unreliable operation, but because it is the one most directlyrelated to the operation of the wholesale markets, it is the only one considered inPart 2.1Two aspects of reliability are always contrasted. Security is the systems abilityto withstand sudden disturbances, while adequacy is the property of having enoughcapacity to remain secure almost all of the time. Part 2 focuses on adequacy andassumes that security requirements will be met if the system has adequate planningreserves. Requirements for operating reserves, which are intended to providesecurity, are of interest here mostly because of their role in raising price, stimulatinginvestment, and thereby contributing to adequacy. This role is often overlookedbecause, under regulation, these requirements were unrelated to adequacy.Chapter Summary 2-3: Operating reserves can be purchased directly by thesystem operator, but the market must be induced to provide adequate planningreserves. The first step in analyzing the markets effectiveness is to find whatdetermines the optimal level of installed capacity. Under a simple but useful modelof reliability, installed capacity is found to be optimal when the duration of loadshedding is given by the fixed cost of a peaker divided by the value of lost load.Section 1: Operating Reserves and Contingencies. A contingency is apossible or actual breakdown of some physical component of the power system.Typically, some operating generator becomes unavailable, leaving the systemFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Wedont know what thehell it is, but its very largeand it has a purpose. Dr. Heywood Floyd2001, A Space Odyssey1968Chapter 2-4Limiting the Price SpikesWHEN SUPPLY CANNOT EQUAL DEMAND, THE MARKET CANNOTDETERMINE A PRICE. When contemporary power markets have enough installedgeneration capacity (ICap) to prevent this market failure at all times, they have somuch that generators cannot cover their costs. This contradiction occurs only forcertain combinations of supply, demand curves and load-duration curves, but whenit does occur, the market fails; there is no long-run equilibrium. Most current powermarkets may well satisfy the conditions for this failure.The demand-side flaws are the cause of this market failure, but they need notbe eliminated in order to remove it. Failure can be prevented simply by reducingthe severity of the first demand-side flawby increasing demand elasticity. Untilthis is accomplished, the systemoperator must set the market price when the marketfails to clear. At these times, some regulatory rule must be adopted for determiningwhat price to set. If price is set only for these few hours, it must be set extremelyhigh, so it may be better to set price more often and lower. Such details are consid-ered in subsequent chapters. The purpose of this chapter is to explain why all currentpower markets need and have price limits.FERC approved price limits of $750, $500 and $250/MWh for Californiabetween 1998 and August 2001. In the summer of 2000 it reduced the NY ISOslimit from its previously approved level of $10,000 to $1,000/MWh bringing itin line with PJ Ms limit. A year later it limited prices indirectly in the West toroughly $100/MWh. In between it suggested that what Western markets reallyneeded was no price limit at all. The Australians tell us prices must be capped atthe value of lost load, which they put at between $15,000 and $25,000/MWh AU.The new electricity trading arrangement in England allows much higher prices andpromptly set a record of over $50,000/MWh. Settling on a reasonable policy willrequire understanding the nature of failure in power markets.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. For a discussion of generation adequacy and VOLL pricing in the U.S. context, see Hirst and Hadley(1999).Fifteen years ago I used charred paper and card in theconstruction of an electric lamp on theincandescent principle. I used it too in theshapeof a horse-shoeprecisely as you say Mr. Edisonis now using it.Joseph Swanin a letter to Nature, January 1, 1880Thereyou haveit. No sooner does a fellow succeed in making a good thing than someotherfellows pop and tell you they did it years ago.Thomas Edisonin replyChapter 2-5Value-of-Lost-Load PricingSHEDDING LOAD IS AN EXPENSIVE WAY TO CURB DEMAND. It makesno distinction between those who need the power most and those who need it least.Because most customers usage is not metered in real time, and because most donot know the price, contemporary markets have little ability to ration demand withprice. Instead, when it is necessary, the system operator must ration demand byshedding load. In this case, the value of another megawatt of power equals the costimposed by involuntary load curtailment. This value is called the value of lost load,VOLL.Basic economic theory says it is efficient to pay suppliers the value of supplyinganother unit of output. Because VOLL is very high, perhaps above $10,000/MWh,this implies a very high price whenever load must be shed. Implementing this policycauses extreme price spikes, but these will be brief and lead to optimal investmentin generating capacity and optimal reliability.1 Although basic theory ignores riskand market power, it provides valuable insights and a basis for discussing moresubtle theories of setting energy prices.Chapter Summary 2-5: Because of the two demand-side market flaws, powermarkets are not yet able to use market forces to determine an appropriate reliabilitylevel. Some authority must estimate VOLL or some other determinant of optimalreliability. All such approaches are based directly or indirectly on VOLL, so theconsequences of error in the estimated value of VOLL cannot yet be avoided. Theseconsequences are not dramatic and can be reduced by overestimating VOLL. Pricerisk and market power are negative side effects of VOLL pricing.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. This plant preceded Edisons invention of the electric light and opened three years before EdisonsPearl Street power stationthe first central station. Charles Brush lit Broadway, New York fromacentral station in 1880. (See http://www.pge.com/009_about/past/&e=921.)By September [1879] a littlebuilding at Fourth and Market was completed and two tiny Brusharc-light dynamos wereinstalled. Together they could supply 21 lights. Customers wereluredby theunabashed offer of servicefrom sundown to midnight (Sundays and holidays excluded)for $10 per lamp per week. Yet in light-hungry San Francisco, customers cameclamoring. Bythefirst of thenext year, four moregenerators with capacity of morethan 100 lights had beenadded. Electricity had cometo theWest.1Pacific Gas and ElectricOur HistoryChapter 2-6Operating-Reserve PricingOPERATING RESERVES ARE NEEDED TO SOLVE VERY SHORT-RUNRELIABILITY PROBLEMS, BUT THEIR PRICING CONTROLS THE LONGRUN AS WELL. Engineering suggests appropriate levels for operating reserves,but it cannot, on its own, determine what price to pay for them. Surprisingly, theirprice should depend on the value of lost load (VOLL) and on long-run, more thanshort-run, reliability considerations. By setting prices to a relatively modest levelwhen the system is short of operating reserves, rather than to the extremely highvalue of VOLL when the system is short of capacity, operating-reserve (OpRes)pricing can substitute for VOLL pricing. This opens up a wide range of policyoptions which can be used to solve some of the most pressing problems of todayspower markets.1Chapter Summary 2-6: A market with randomshifts in the annual load-durationcurve is examined to compare the side effects of high and low price spikes. Highprice spikes are found to cause investment risk and to encourage the exercise ofmarket power. Low spikes are just as effective as VOLL pricing at encouragingoptimal investment in generation capacity. High price spikes are more useful onthe demand side than on the supply side, so different price limits should be usedfor the two sides of the market.Section 1: Less Risk, Less Market Power. In a market with two load-durationcurves, one for hot years and one for normal years, short-run profits are foundto fluctuate between zero and 400% of normal under VOLL pricing but onlyFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.An electrick body can by friction emit an exhalation so subtile, and yet so potent, as by its emissionto causeno sensiblediminution of theweight of theelectrick body, and to beexpanded through asphere, whosediameter is abovetwo feet, and yet to beableto carry up lead, copper, or leaf-gold, atthedistanceof about a foot from theelectrick body.Sir Isaac NewtonSamuel Johnsons Dictionary of the English Language, 1755Chapter 2-7Market Dynamics and the Profit FunctionECONOMICS FOCUSES ON EQUILIBRIA BUT HAS LITTLE TO SAY ABOUTTHE DYNAMICS OF A MARKET. Once economics shows that a system has anegative feedback loop so that there is a point of balance, it considers its job done.Engineers move beyond this stage of analysis to consider whether a system willsustain oscillations and, if not, whether it is over- or under-damped. Economicsunderstands that investment dynamics can produce cycles but has faith thatrationality will generally prevent this. It also ignores the noise sources (randomlyfluctuating inputs) that keep economic systems excited.Usually these oversights do not offer much cause for concern. In power markets,however, a 4 or 5% fluctuation in either load or capacity, coupled with the wrongpricing policy, can cause the average annual spot price to triple. Such dynamicscannot be ignored. If they are not corrected at the time of market design, they willbe reported later by the press.Many profit functions determine the same optimal equilibrium value of installedcapacity, but this means only that they agree at one point. At other points, they maydiffer dramatically, and these differences imply different market dynamics. Al-though the profit function falls far short of providing a theory of those dynamics,it does provide some basic insights which make possible a discussion of the topic.Chapter Summary 2-7: Profit functions can be calculated fromthe load durationcurve and two policy variables: the price cap and the required level of operatingreserves. Once calculated they reveal the equilibrium level of installed capacityand give some indication of the markets riskiness and conduciveness to the exerciseof market power. Thus the first step in assessing a pricing policy should be thecalculation of the associated profit function.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. This wind generator was constructed by Charles Brush for his personal use. The article begins by notingthat After Mr. Brush successfully accomplished practical electric illumination by means of arc lights,incandescent lighting was quickly brought forward and rapidly perfected.Theshaft is 20 feet long and 6 1'2 inches in diameter. Thewheel, which is 56 feet in diameter [is]provided with 144 blades twisted likethoseof screw propellers. Thesail surfaceis about 1,800squarefeet. Thespeed of thedynamo at full load is 500 revolutions per minute, and its normalcapacity at full load is 12,000 watts. Theworking circuit is arranged to automatically closeat75 volts and open at 70 volts. Theamount of attention required to keep it in working conditionis practically nothing. It has been in constant operation morethan two years.1Scientific AmericanDecember 20, 1890Chapter 2-8Requirements for Installed CapacityPRICE SPIKES ENCOURAGE INVESTMENT INDIRECTLY; A CAPACITYREQUIREMENT GETS RIGHT TO THE POINT. The capacity approach is definedby two regulatory parameters but, as has been demonstrated, so is the price-spikeapproach. Both can induce any desired level of reliability while preserving thecorrect mix of technology, so the choice between them should be based on theirside effects.1Chapter Summary 2-8: A capacity requirement produces an easily controlled,low-risk profit function. It can be combined with a price-spike approach to producea profit function that is still relatively low risk while providing high prices at a fewcrucial times to tap existing high-priced resources. Combining price-spike andcapacity-market profit functions does not increase equilibrium profits, but it doesincrease the equilibrium value of installed capacity unless the two policies areproperly adjusted. Adjustment requires taking account of random fluctuations inthe level of installed capacity.Section 1: The Capacity-Requirement Approach. All load-serving entitiesare required to own, or to have under contract, a certain required capacity. The sumof these is the markets installed capacity (ICap) requirement and is typically about18% greater than annual peak load. A load-serving entity is penalized if it fails tomeet its requirement.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. Cournot anticipated J evons, Menger, and Walras in discovering the law of one price and otherneoclassical results. J evons (1835-1882), with his publication of The Coal Question in 1865, was the firstto draw attention to the imminent exhaustion of energy supplies. In 1870 he invented the logical piano,the first machine to solve problems faster than a human.In thesameopen market, at any moment, therecannot betwo prices for thesamekind of article.W. Stanley Jevons TheTheory of Political Economy1879Therearetwo fools in every market; oneasks too little, oneasks too much. Russian proverbChapter 2-9Inter-System Competition for ReliabilityMARKETS WITH LOW PRICE CAPS HAVE LITTLE PROTECTION FROMCOMPETING MARKETS WITH HIGH PRICE CAPS. At crucial times, the high-cap market will buy up the reserves of the low-cap market. This can cause a groupof competing markets to evolve toward a risky high-priced regulatory approach.Competing systemoperators are not led by an invisible hand to the optimal policy.This chapter uses previously developed models and tools to investigate whathappens when pairs of markets, operating under different pricing rules, competefor energy and capacity.1Chapter Summary 2-9: Competition between markets with different price capswill favor the market with the higher cap. The lower-price-cap market will spendas much on inducing investment but will find its reserves bought out from underit at crucial times by the high-price-spike market. The result will be competitionbetween system operators for the higher price cap unless a regional regulatorprevents this. Capacity-requirement markets can solve a similar problem by requir-ing capacity rights to be sold on an annual basis.Section 1: Price-Cap Competition. A VOLL market and OpRes market,identical except for their pricing policies, are modeled as able to trade energy andoperating reserves. The result is that when load is expected to be high, moregenerators sell power and reserves to the VOLL market. This equalizes the expectedshort-run profits in the two markets; as a result the OpRes market suffers reducedreliability. This will force it to adopt a higher price cap to protect itself from inter-system competition.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Theday when weshall know exactly what electricity is, will chroniclean event probablygreater, moreimportant than any other recorded in thehistory of thehuman race. Thetimewillcomewhen thecomfort, thevery existence, perhaps, of man will depend upon that wonderfulagent.Nikola Teslac. 1893Chapter 2-10Unsolved ProblemsLOW PRICES, EVEN THOSE ONLY 200% ABOVE NORMAL, CAN INDUCEINVESTMENT, BUT THEY CANNOT INDUCE CURTAILMENT OF HIGH-VALUE LOAD. Neither can they induce supply from the odd high-marginal-costgenerator nor from a generator that is producing in its emergency operating range.The problems of low price caps have nothing to do with adequate investment ingenerating capacity. They concern only the short-run responses of high-value loadand high-marginal-cost supply. These problems are small compared with theproblem of long-term market stability and generation adequacy, but they are worthsolving. This chapter defines them and suggests steps toward solutions.Chapter Summary 2-10: Genuinely high-marginal-cost power should bepurchased in a market separate from the regular supply market and with its ownhigh price cap. Load reductions, most of which have high marginal values, shouldbe purchased at a price that is allowed to exceed the price cap in the supply market.The (relatively) low price cap of the supply market should be set regionally andenforced strictly to prevent out-of-market purchases.Section 1: High Marginal Costs and Low Price Caps. Several small sourcesof high-marginal-cost power make high prices worthwhile. To avoid disruptiveside effects, these should be restricted to an emergency power market that catersonly to high-cost sources. The problem is to select only these sources and limitmarket power under a high price cap. An adequate solution appears to be withinreach.Section 2: Pricing Supply and Demand Separately. Allowing demand-sideprices to rise above the supply-side cap makes use of existing demand responsive-ness and stimulates the development of greater elasticity. This requires a methodof setting price higher than any supply bid and of refunding the extra revenuecollected.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Theconclusion seventeen years later, is essentially thesame. . . industries differ onefrom theother, and theoptimal mix of institutional arrangements for any oneof them cannot bedecidedon the basis of ideology alone. Thecentral institutional issueof public utility regulationremains . . . finding thebest possiblemix of inevitably imperfect regulation and inevitablyimperfect competition. Alfred E. KahnTheEconomics of Regulation1995Chapter 3-1IntroductionREAL-TIME TRANSACTIONS REQUIRE CENTRAL COORDINATION;WEEK-AHEAD TRADES DO NOT. Somewhere in between are dividing lines thatdescribe the system operators diminishing role in forward markets. Where to drawthose lines is the central controversy of power-market design. A related controversy,not considered in Part 3, is how finely the system operator should define locationalprices. Those who favor a large role for the system operator in one sphere tend tofavor it in others. Thus the controversies of market architecture have a certainconsistency. Although the rhetoric focuses on how centralized a design is, the litmustest in most of the controversies is the extent of the system operators role. Thistoo may be a distraction. A larger role for the system operator implies a smallerrole for profitable enterprises. One side fears the inefficiency and market-powerabuses of private parties playing social roles. The other side fears the inefficiencyof nonprofit organizations but also covets the central market roles played by thesystem operator. Power markets present unusually acute coordination problems. They are theonly markets that can suffer a catastrophic instability that develops in less than asecond and involves hundreds of private parties interacting through a shared facility.The extent and speed of the required coordination are unparalleled. Generators2000 miles apart must be kept synchronized to within a hundredth of a second.Such considerations require a market that in some respects is tightly controlled inreal time. Historically, this control has extended to areas far from the precariousreal-time interactions. As deregulation brings markets into new areas, it is notsurprising to find the proponents of markets reaching beyond their ability and tofind the traditional system-control structure attempting to perpetuate now unneces-sary roles for itself. This clash of interests has produced much heat and shed littlelight.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. Maxwell developed the mathematics of electromagnetic fields, later used to design AC motors,transformers, and power lines. He predicted the possibility of electromagnetic waves and calculated theirtheoretical velocity fromlaboratory measurements on electric and magnetic fields. At first his suggestionthat light is electromagnetic was dismissed as a not wholly tenable hypothesis.Wecan scarcely avoid theinferencethat light is thetransverseundulations of thesamemediumwhich is thecauseof electric and magnetic phenomena.James Clerk Maxwell1861This velocity is so nearly that of light, that it seems wehavestrong reasons to concludethat lightitself (including radiant heat, and other radiations if any) is an electromagnetic disturbanceintheform of waves propagated through theelectromagnetic field according to electromagneticlaws.11864Chapter 3-2The Two-Settlement SystemTHE REAL-TIME PRICE ALWAYS DIFFERS FROM THE DAY-AHEADPRICE. WHICH IS IN CONTROL? Day-ahead (DA) prices, and especially earlierprices, differ significantly from the corresponding real-time (RT) price. Thedifferences are due to misestimations made before traders know all the details ofthe RT conditions. In a competitive market the RT prices are true marginal costprices, and the forward prices are just estimates, sometimes very rough estimates.With most trade occurring in the forward markets, does this imply that only a smallproportion of generation is subject to the correct incentives? Not under a propertwo-settlement system. The purpose of the RT market is to correct the predictionerrors of the past. If the transaction costs in this market are minimized so thatprofitable trade is maximized, the RT price will be accurate and will control actualproduction. Past mistakes have financial impacts but will not cause inefficiencywhich is a purely physical phenomenon.1Contracts for differences (CFDs) insulate bilateral trades from all risks of spotprice fluctuations while allowing the inevitable inefficiencies of forward tradingto be corrected by accurate RT price signals. Both the two-settlement system andCFDs allow efficient re-contractinga standard economic solution to the problemsof decentralized forward trading. Advocates of bilateral trading have often failedto recognize this point and have opposed the very mechanisms that make decentral-February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. The universe is governed by four forces and matter is made of their associated particles. The electronand photon are the carriers of the electromagnetic force, and the other three forces are gravity, the weakforce and the nuclear force. Maxwell discovered the mathematics of the electromagnetic force, Einsteinthe mathematics of the gravitational force, and Feynman the laws of the weak force which he unified withthe electromagnetic force.From a long view of the history of mankindseen from, say, ten thousand years fromnowtherecan belittledoubt that themost significant event of the19th century will bejudgedas Maxwell's discovery of thelaws of electrodynamics.Richard FeynmanOnescientific epoch ended and another began with James Clerk Maxwell.1Albert EinsteinChapter 3-3Day-Ahead Market DesignsCENTRAL DAY-AHEAD MARKETS CAN BE DESCRIBED AS AUCTIONS.The most obvious design sets energy prices based on simple energy-price bids. Adifferent approach turns the system operator into a transportation-service providerwho knows nothing about the price of energy but sells point-to-point transmissionservices to energy traders.1Either of these approaches presents generators with a difficult problem. Somegenerators must engage in a costly startup process (commitment) in order to produceat all. Consequently, when offering to sell power a day in advance, a generator needsto know if it will sell enough power at a price high enough to make commitmentworthwhile. Some day-ahead (DA) auctions require complex bids which describeall of a generators costs and constraints and solve this problem for the generators.If the system operator determines that a unit should commit, it ensures that all itscosts will be covered provided the unit commits and produces according to theaccepted bid. Such insurance payments are called side payments, and their effecton long-run investment decisions is considered in Sections 3-9.3 and 3-9.3.Chapter Summary 3-3: Day-ahead markets run by system operators are runas auctions. Although some trade energy, some sell transmission, and some solvethe unit-commitment problem, they all use the same philosophy for choosing whichbids to accept and for setting prices. Four archetypical markets are summarized:(1) a power exchange, (2) a transmission-rights market, (3) a power pool, and (4)PJ Ms DA market which mixes all three.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Electric energy thus is themost useful form of energyand at thesametimeit is the mostuseless. [It] is never used as such . . . [but] is theintermediary.Charles Proteus SteinmetzHarpersJanuary 1922Chapter 3-4Ancillary ServicesPOWER IS THE PRIMARY SERVICE, BUT SIX ANCILLARY SERVICES ARENEEDED TO ENSURE RELIABLE, HIGH-QUALITY POWER, EFFICIENTLYPRODUCED. Usually ancillary services are defined by how they are provided ratherthan by the service rendered. This results in a plethora of services and little insightinto their relationship to market design. Defining services by the benefit theyprovide and defining thembroadly produces a short but comprehensive list. Servicesdirected at long-term investment are not counted as ancillary to real-time (RT)power delivery. The six listed services require planning by the system operator,but economic dispatch is jointly provided by the system operator and the market.How that task is shared should be the subject of intense debate. Chapter Summary 3-4: Of the six ancillary services, the system operator orits agent must directly provide transmission security and trade enforcement, andto some extent economic dispatch. The other services, balancing, voltage stability,and black-start capability can be purchased from a competitive market, but thesystem operator must demand and pay for these services.Section 1: The List of Ancillary Services. Services are defined by the benefitthey provide to the market and its participants, not by their method of provision.An accurate frequency is required by some motors and particularly by large genera-tors. Many appliances need a fairly accurate voltage, and together these two servicesdefine the provision of power from the customers perspective. Transmissionsecurity and occasionally black-start capability are indirect services needed by themarket to provide the first two. Economic dispatch can include the solution of theunit commitment problem and often includes efficiently dispatching around conges-tion constraints. Trade enforcement is required to provide property rights essentialfor bilateral trading.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Economic questions involvethousands of complicated factors which contributeto a certain result.It takes a lot of brain power and a lot of scientific data to solvethesequestions. Thomas Edison1914Chapter 3-5The Day-Ahead Market in TheoryTHE DAY-AHEAD MARKET IS THE FORWARD MARKET WITH THEGREATEST PHYSICAL IMPLICATIONS. By providing financial certainty, it canremove the risk of incurring startup expenses. The more efficient the market, themore accurate the startup decisions and the lower the cost of power. Even withoutthe unit-commitment problem, reducing financial risk would reduce the cost ofcapital.As explained in Chapter 3-3, the day-ahead (DA) market can utilize one of threebasic architectures or a combination. Bilateral markets, exchanges and pools caneach provide hedging and unit commitment. The controversy over the choice ofarchitecture is driven by concerns over the shortcomings of private markets andnonprofit system operators in performing the coordination functions associatedwith unit commitment. Hedging is also an issue as pools claim to provide it morecompletely than exchanges.Some theory of market clearingwhen it is possible and when nothelps toprovide a framework for evaluating the various designs. Nonconvex productioncosts are the key to this theory, and while conceptually arcane, the focus of currentcontroversy and volumes of market rules attest to their impact on market design.Chapter Summary 3-5: Nonconvex generation costs violate an assumptionof perfect competition, but the magnitude of the resulting problems is unknown.The pool approach is designed to minimize these problems, but its pricing ignoresinvestment incentives. The bilateral approach faces formidable coordinationproblems in the DA market. It may be less efficient and provide less reliability thana centralized approach. Side-payments made by a DA pool do not increasereliability.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. Although the lack of a market clearing price is indicated by a static analysis, the dynamics of a powermarket which are limited by ramping constraints may reverse this conclusion.2. See Rothwell and Gomez (2002) for descriptions of Norwegian, Spanish, and Argentinian spot markets.It must bedonelikelighting. Ben JohnsonEvery Man in his Humour1598 Chapter 3-6The Real-Time Market in TheoryUNLIKE A DAY-AHEAD EXCHANGE, A REAL-TIME EXCHANGE CANNOTUSE BIDS. The real-time (RT) market consists of trades that are not undercontractpower that just shows up, or is taken, in real time and accepts the spotprice. An RT exchange works like a classical Walrasian auction. A price is an-nounced and suppliers and customers respond. If the market does not clear, a newprice is announced. The difference is that in a power market trade takes place allthe time; there is no waiting to trade until the right price is discovered. Like aWalrasian auction and unlike a day-ahead (DA) exchange, an RT exchange mayfind there is no price that balances supply and demand.1 Consequently, if anexchange is used, it must be supplemented with another exchange or perhaps anoperating-reserve market in the form of a pool. There are many possibilities, andlittle is known about their relative merits.2Chapter Summary 3-6: Pure bilateral markets are too slow to handle RTbalancing and transmission security. A centralized market is needed which cantake the pool approach, the exchange approach, or something in between. Poolshave an easier time achieving a supply-demand balance than do exchanges becausethey utilize different prices for different generators. This allows them to offer anoption in a forward market that depends on the real-time market price. An RTexchange can achieve a similar effect but only by employing one or more additionalexchanges. These could be for detrimental generation or operating reserves.Alternatively an operating-reserve pool could supplement an RT exchange.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. Only 26,771 MW submit DA multipart bids, while 30,031 MW proves to be necessary in real time.Predicting is pretty risky business, especially about thefuture.Mark Twain(18351910)Chapter 3-7The Day-Ahead Market in PracticeIS THE DAY-AHEAD POOL PRICE DETERMINED BY ARBITRAGE ORCOMPUTATION? Forward prices are usually determined by arbitrage betweenthe forward market and the real-time (RT) market. Day-ahead (DA) markets areforward markets, but DA pools with multipart bids have been promoted for theirability to determine through computation the optimal dispatch and the efficientprice. Both theories might prove true, or half true, but more likely one is essentiallyright and the other wrong.There is no question that the computation takes place accurately and in amechanical sense determines the DA pool price. The result of the computation isalso determined by its inputs. Because the computation itself is a fixed procedure,while the input changes daily, it may be best to view the pool price as determinedby inputs. Then the question becomes: Do the pools input data accurately reflectthe producers reality, or do they deliberately misrepresent that data in order totake advantage of arbitrage opportunities. In the first case, the pool calculationmakes use of good input data to produce a price that reflects the true details ofgeneration costs. In the second case, the calculation is not a sensible unit-commit-ment calculation because its inputs are false. The bidders have manipulated thepools computation, and the outcome may be thought of as being determined byarbitrage.Unfortunately, it takes only a small percentage of arbitragers to dominate theoutcome. In PJMs DA market, 11% of the generators that are needed, and eventu-ally produce power, in the RT market are rejected by the unit commitment calcula-tion (PJ M, 2001, 30).1 This alone proves the calculation is not highly accurate.Morever, while 3,260 MW of multipart bids representing needed generation arerejected, 6,169 MW of supply-side arbitrage bids (one-part bids) are accepted onFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Wherethereis much light, theshadows aredeepest.GoetheWilhelm Meisters Apprenticeship1771Chapter 3-8The Real-Time Market in PracticeWHEN MARGINAL-COST PRICES WONT CLEAR THE MARKET, ARETHEY STILL THE RIGHT PRICES? When production costs are nonconvex,as are startup and no-load costs, competitive market theory predicts the market maynot clear, marginal-cost prices may not be optimal, and the market may not beefficient. The sole purpose of the multipart bids used by power pools is to overcomeproblems caused by nonconvex costs. The pool approach recommends setting themarket price equal to marginal cost exactly as if there were no problem and thenmaking side payments to generators who are needed for the optimal dispatch. Thesepayments cover only the costs that marginal-cost prices fail to cover.The pool approach recognizes the first failure of marginal-cost pricing andcorrects it with side payments. But true competitive prices do more than minimizeproduction costs; they send the right signals (1) to consumers and (2) to investorsin new generation. Can a power pools combination of marginal-cost prices andside payments replicate these benefits of competitive prices? Using an examplefrom a dispute over NYISOs pricing, this chapter shows that pool pricing failsboth of these tests. Surprisingly, it was NYISOs position that standard marginal-cost pricingpool pricingwas inefficient for at least five reasons. Pool prices are neither the prices of Adam Smith, nor those of competitiveeconomics. They are not right for the demand side and they are not right for long-run investment. Pool prices are right for the centralized solution of the problemof minimizing short-run production-costs, given an output level that is incorrectlydetermined when demand is elastic.This does not mean the pool approach is a bad idea; it simply means thatadopting it because it gets the prices right would be naive. The problem ofnonconvex costs is difficult and a complex market design, such as a pool, couldFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Let us not go over old ground, let us rather preparefor what is to come.Marcus Tullius Cicero(10643 B.C.)Chapter 3-9The New Unit-Commitment ProblemTHE OLD PROBLEM ASKS WHICH UNITS SHOULD BE COMMITTED; THENEW PROBLEM ASKS WHAT MARKET DESIGN WILL BEST SOLVE THEOLD PROBLEM. The old problem was solved by collecting data on all the genera-tors and applying the techniques of mathematical programming. The new problemmight be solved by a market designed to induce generators to voluntarily andaccurately provide this same data. The market coordinator could then purchasepower from the generators identified by the old algorithm. This is the power-poolapproach. A power exchange is an alternative approach which pretends the oldproblem does not exist.It seems impossible that ignoring the old problem could be the best way to solveit, but most market architectures ignore just such complex commitment problems.When the market coordinator ignores the problem, the suppliers take it up, and theymay do a remarkably good job. Although the programming techniques used to solvethe old problemare astoundingly complex, most generators can get the right answeron most days simply by looking at the calendar. If you have a baseload plant andits summer, keep your plant committed. If you have a peaker, dont look at thecalendar, just watch the real (RT) priceday-ahead (DA) forecasts are not needed.When it really matters, on the hottest days, every supplier knows to commit. Butthose who commit units for individual suppliers will do much better. They willhave years of experience and the necessary resources. Moreover, they may haveaccess to an exchange that uses two-part prices or multiple rounds of bidding. Tobeat a good exchange market, a pool must be very good indeed.Two central concerns have motivated the power-pool approach: efficiency andreliability. Committing the wrong units costs more, but this problem is limited bythe magnitude of the cost involved and the efficiency of markets without centralizedunit commitment. Reliability is more of a wild card. Perhaps a decentralized marketFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.A Telegraphers Valentine, by James Clerk Maxwell, 1860.Thetendrils of my soul aretwinedWith thine, though many a mileapart.And thinein closecoiled circuits windAround theneedleof my heart.Constant as Daniel, strong as Grove.Ebullient throughout its depths likeSmee,My heart puts forth its tideof love,And all its circuits closein thee.O tell me, when along thelineFrom my full heart themessageflows,What currents areinduced in thine?Oneclick from theewill end my woes.Through many a volt theweber flew,And clicked this answer back to me;I am thy farad staunch and true,Charged to a volt with lovefor thee.Chapter 3-10The Market for Operating ReservesA MARKET FOR OPERATING RESERVES PAYS GENERATORS TO BE-HAVE DIFFERENTLY FROM HOW THE ENERGY MARKET SAYS THEYSHOULD. If generators are cheap and will produce at full output, the market mighttell them to produce less. If they are too expensive to produce at all, it may tell themto start spinning, and this may require them to produce at a substantial level. Itspurpose is to increase reliability and moderate price spikes.Chapter Summary 3-10: Not maximizing profits has an opportunity cost, andgenerators must be paid for this to secure their cooperation. There are two philoso-phies: (1) have the system operator calculate this value from the real-time priceand pay them accordingly; (2) have the generators guess this value and includeit in their bids. The first approach may be quite susceptible to gaming while thesecond is optimal in theory but risky for generators in practice and may increasethe randomness of the outcome.Section 1: Types of Operating Reserve. Operating reserves come in severalqualities classified by how quickly the generator can respond. Regulation keepsthe system in balance minute by minute. Ten-minute spinning reserve can startresponding almost instantly and deliver its full response within ten minutes. Thistype of reserve will serve as a model for considering market designs. The problemof linking the different reserve markets is not considered.Section 2: Scoring by Expected Cost. One approach to conducting a marketfor spin is to have suppliers submit two-part bids, a capacity price, CCbid, and anenergy price, VCbid. An obvious way to evaluate such bids is to score them by theirFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Sixty minutes of thinking of any kind is bound to lead to confusion and unhappiness.James Thurber(1894-1961)Chapter 4-1Defining Market PowerMARKET POWER, A CENTRAL TOPIC IN ECONOMICS, HAS BEENDEFINED CAREFULLY. The standard economic definition is a central conceptof industrial organization. Market power is the ability to alter profitably prices awayfrom competitive levels. This definition, with slight variations, has probably beenin use for more than a hundred years and is supported by a large body of empiricaland theoretical work. It is terse and carefully worded as a good technical definitionshould be. Frequently, regulators ignore it and attempt their own definition. FERCannounced a new one in its report, State of the Markets 2000. By the end of 2001it had been discarded and a new one was under design.Market power is defined as the ability to withhold capacity orservices, to foreclose input markets, or to raise rival firms costsin order to increase prices to consumers on a sustained basiswithout related increases in cost or value. (FERC 2000a)Market power is a three step process: (1) an exercise, (2) an effect on price andquantity, and (3) an impact on market participants. The first step can take on manyforms and appearances. For clarity, the economic definition considers only price(step 2) and profit (step 3). FERCs definition focuses on step 1 and misses somemethods of exercise such as raising the offer price of a supply bid. Because it omitsprofitably, all baseload plants would have market power whenever they areneeded even though they would lose money if they exercised it. It ignores theconcept of competitive price. It adds the clause without related increases incostany time a supplier exercises market power it is trying to recover somerelated increase in cost. The notion of sustained basis may exclude peakersand is vague. No authority is cited for this definition.Both the FERC definition just cited and the revisions to it under considerationin January 2002 include the concept of raising competitors costs. In a nontechnical,February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Peopleof thesametradeseldom meet together, even for a merriment or diversion, but theconversation ends in a conspiracy against thepublic, or in somecontrivanceto raiseprices.Adam SmithTheWealth of Nations1776Chapter 4-2Exercising Market PowerMONOPOLY POWER ALWAYS RESULTS IN COMPETITIVE SUPPLYBEING GREATER THAN DEMAND AT THE MARKET PRICEA POSITIVEQUANTITY WITHHELD. This signature of market power must be checked todetermine the nature of any observed price increase and to determine its signifi-cance. A market that cannot tolerate a few hundred megawatts of withholdingcannot withstand a hot afternoon or a generator outage. Such a market should beshut down and redesigned.Chapter Summary 4-2: Market power should be looked for only in the real-time(RT) markets. It should be looked for among inframarginal as well as marginalgenerators. The amount of withholding should always be examined along with theprice increase.Section 1: Market Power and Forward Markets. If prices in a forwardmarket are too high, customers can wait for the next forward market or for real time.In the RT market they can wait no longer. Consequently, market power cannot beexercised in forward markets; this includes day-ahead (DA) markets. Market powerexercised in real time is reflected into forward-market prices through arbitrage.Section 2: Long-Run Reactions to Market Power. The threat of new supplyentering can discipline the exercise of market power because those exercising itfear high prices will attract too many future competitors. Suppliers may also chooseto exercise less market power for fear of retaliation by regulators.Section 3: Marginal and Inframarginal Market Power. Frequently thegenerator that sets the market price is not the one exercising market power. Oftenit is some inframarginal generator, possibly one that would be marginal had it notpriced itself out of the market.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Merchants areoccupied solely with crushing each other:such is theeffect of freecompetition.Charles Fourier(1772-1837)Likemany businessmen of genius helearned that freecompetition was wasteful,monopoly efficient.Mario PuzoTheGodfather1969Chapter 4-3Modeling Market PowerMODELING MARKET POWER HELPS EXPLAIN THE FACTORS THATCONTROL THE EXERCISE OF MARKET POWER. The models, however, arenot accurate predictors of market power. Except in the case of pure monopoly,market power is not well understood because it involves strategic behavior byseveral competitorsan oligopoly. Game theory is subtle, and the game ofoligopolistic competition has complex rules. By abstracting from much of itscomplexity, models of market power explain its main features.Elasticity of demand is the most important factor in present power markets. Thedistribution of the size of competitors is also a key factor. Even this is extremelyhard to compute in a power market because it depends on barriers to trade whichare very complex and vary continuously, often dramatically. The style of competi-tion is also crucial. Economics can model competition based on price or quantity,but in power markets suppliers compete using supply curves that combine thetwo. The theory of supply-curve competition (discussed in Chapter 4-4), whilepromising, is not yet well developed.Chapter Summary 4-3: The market power of a monopolist is limited bydemand elasticity. An oligopolys market power is also limited by the number andrelative size of competitors. Market share is a suppliers sales divided by total tradein the market. The sum of the squares of market shares is called theHerfindahlHirschman Index (HHI) and is one of three factors determining marketpower in the Cournot model.Section 1: Monopoly and the Lerner Index. A monopolist will raise priceto maximize profit but could raise it even higher. The more customers respond tohigh prices by curtailing demand, the less a monopolist will raise the price. TheFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Monopoly, in all its forms, is thetaxation of theindustrious for thesupport of indolence,if not of plunder. John Stuart MillPrinciples of Political Economy1848Chapter 4-4Designing to Reduce Market PowerMARKET POWER CAN BE CONTROLLED BY COMPETITION OR BYMONITORING AND ENFORCEMENT. Competition is preferable but does notautomatically reach satisfactory levels. The four key determinants of the competi-tiveness of a power market are: (1) demand elasticity, (2) supplier concentration,(3) the extent of long-term contracting, and (4) the extent of supply-curve bidding.All four of these are partially susceptible to regulatory policy and/or marketdesign. None are particularly easy to affect, with the exception of the systemoperators demand elasticity for operating reserves which translates directly intoelasticity of demand for power. Since lack of demand elasticity is the primary sourceof market power in the industry, this simple change is long overdue. Fortunately,demand elasticity of large customers is also relatively easy to increase, once policymakers understand its importance and how to minimize the risks of real-time (RT)pricing.Supplier concentration is quite difficult to decrease, but merger policy shouldprevent its increase at least until the demand elasticity problem has been fixed.There is little theory on how to increase long-term contracting except at the timeof divestiture when vesting contracts can be required. Supply-curve bidding isnaturally encouraged by uncertainty in the demand level. A bid that must span theentire day effectively increases this uncertainty. Supply-curve bids tend to be veryelastic at lower output levels and very inelastic at high output levels, which explainswhy power markets have relatively little trouble with market power off peak.Research is needed to find a policy to harness this effect.Chapter Summary 4-4: An ounce of prevention is worth a pound of cure andstrengthening the normal forms of market-power mitigation may be the best formof prevention. Demand elasticity tops the list. Forward contracting should beFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.A friend in themarket is better than money in thechest.Proverbcollected in Thomas Fuller, Gnomologia1732Chapter 4-5Predicting Market PowerSTANDARD WISDOM HOLDS THAT HHIS BELOW 1000 ARE CER-TAINLY SAFETHEY ARE NOT. The HHI accounts for only one factor, concen-tration, out of five key economic factors that determine the extent of market power.The other four, demand elasticity, style of competition, forward contracting, andgeographical extent of the market, can each affect market power by an order ofmagnitude.Chapter Summary 4-5: The HHI misses most of the action in power markets.Cournot models can capture much more but still miss the mark widely. Resultsare often reported in terms of the Lerner index, which frequently reports a declinein marginal cost as if it were an increase in price. A combination of estimatingabsolute market power and predicting relative market power may answer somequestions a little more accurately. These include the impact of mergers, transmissionupgrades and transmission pricing.Section 1: Four Factors which HHI Ignores. The Herfindahl-Hirschmanindex is computed from the market shares of suppliers. It takes no account ofdemand inelasticity which, other things being equal, makes market power at least10 times worse in power markets than in most other markets. It predicts only theLerner index, which is loosely connected to market power. It takes no account ofthe style of competition, the extent of forward contracting, or the geographicalextent of the market.Section 2: Difficulties Interpreting the Lerner Index. While the definitionof market power compares market price with the competitive price, the Lerner indexcompares market price with marginal cost in the uncompetitive market. The Lernerindex combines the effects of reduced marginal cost and increased price. In a powerFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Why is thereonly onemonopolies commission?AnonymousChapter 4-6Monitoring Market PowerDISCOVERING MARKET POWER OFTEN REVEALS MARKET FLAWS.While fixing these flaws, temporary restraints may need to be placed on marketparticipants, but the goal of fixing the market should be kept in focus. If the rulesare flawed, repairs can be made quickly, but when the architecture or structure isflawed, the required changes can take years. Then market monitors are forced tospend too much effort controlling an unruly market.Chapter Summary 4-6: The trick to market monitoring is to ignore vaguedefinitions and rigorously apply the economic definition of market power. If themarket price is above the competitive level, then necessarily, some supplier is notacting as a price takersomewhere there is a gap between the profit-maximizingsupply of a price taker and the actual supply. That gap is termed the quantitywithheld, and it is proof of market power. Observing a high price is not proof,nor is observing a price higher than left-hand marginal cost. Observing the real-time(RT) price above right-hand marginal cost demonstrates short-run withholding.In the RT market, this proves market power, except for unusual cases of opportunitycost such as exhibited by hydrogenerators.Section 1: FERCs Ambiguous Standard. A popular misinterpretation ofthe DOJ /FTC definition of market power, abetted by DOJ s Guidelines, requiresthe price increase to be significant in magnitude as well as duration. FERCsrequirement that no market power be exercised makes sense only under thismisinterpretation; otherwise, the requirement would be an impossibility. As aconsequence, FERCs policies regarding market power are highly ambiguous, andits pronouncements on the need to eliminate all market power cause confusion.Section 2: Market Monitoring. Power markets need monitoring because oftwo structural problems: (1) electric energy cannot be stored, and (2) RT demandFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.ELECTRICITY. n.s. [from electrick. SeeELECTRE.] A property in somebodies, whereby, whenrubbed so as to grow warm, they draw littlebits of paper, or such likesubstances, to them.Samuel JohnsonTheDictionary of theEnglish Language, 1755ELECTRICITY, n. Thepower that causes all natural phenomena not known to becaused bysomething else.Ambrose BierceTheDevils Dictionary, 18811906Chapter 5-1Power Transmission and LossesWATTS MEASURE POWER, BUT VOLTS AND AMPS ARE THE NUTS ANDBOLTS OF ELECTRICITY. The economics of power flows can be understoodwithout their help, yet they underlie every important physical phenomenon in thepower marketplace. This chapter uses them to explain power flow, transmissionlosses, and the reason Westinghouses AC networks triumphed over Edisons DCnetworks.Chapter Summary 5-1: Voltage is pressure and electrical current is like a flowof water; with more pressure, more current flows. Power delivered is voltage timescurrent (volts times amps) and is measured in watts. The power lost in a transmis-sion line of a given voltage is proportional to the square of the power flow, butif the voltage is doubled the same power can be delivered with 1'2 the current and1'4 the loss. Transformers make it easy to raise an AC voltage and this allows thetransmission of power with very little loss.Section 1: DC Power lines. Direct-current power lines, used in the past andagain gaining importance, provide the simplest example of power transmission.Power transfer, W, equals V I, which is the voltage, V, of the transmission linetimes the current flow, I. Transmission losses are proportional to the square of thedelivered power and inversely proportional to the square of the power-line voltage.Consequently, two equal loads cause four times the loss caused by one. This makesa meaningful assignment of losses to loads impossible.Section 2: AC Power lines. In the United States, alternating current (AC)completes a cycle, two reversals of direction, 60 times per second. Transformers,February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Wereset up for direct current in America.Peoplelikeit, and its all Ill fool with.Thomas Edison1884Chapter 5-2Physical Transmission LimitsWITHOUT TRANSMISSION LIMITS, POWER MARKETS WOULD HAVEAMPLE COMPETITION AND NO NEED FOR CONGESTION PRICING. Design-ing power markets would be far easier. A competitive market will only accountfor the physical limits on all power lines and transformers if property rights aredesigned to represent these limitations properly.Transmission limits are of two types: (1) physical limits, and (2) contingencylimits. Physical limits are the basis of the contingency limits, but contingency limitsare stricter and are the relevant limits for trading. A contingency limit ensures thata lines physical limit will not be violated if some other line or generator goes outof service unexpectedly. All limits, whether physical or based on contingencies,can be expressed at any point in time as a simple megawatt limit on power flowthat is allowed over the power line or transformer in question. But contingencylimits present a complex problem for trade because a trade can affect the contin-gency limit on lines it uses. (This problem is not discussed in Part 5.)Two facts about limits are economically important, the megawatt limit itself,and how predictable it is. Unpredictability makes forward trading difficult, andthis chapter explains some of the reasons that limits vary.Chapter Summary 5-2: Power lines have physical limits that restrict the amountof power they are allowed to carry. These limits prevent overheating of the wires,instability of the power flow, and low-voltage conditions at the load end of the lines.Any of these limits can be thought of as a simple limit on real power flow, butbecause the basis of these limits is complex, they may vary according to how thesystem is operating at a particular time.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Thepopular belief is that radium constantly produces heat and light without any appreciablelossin its weight. . . . thereexists a form of energy of which wehaveas yet no knowledge, but whichmay yet becomeavailableto us as a result of further discoveries.George Westinghouse1911Chapter 5-3Congestion Pricing FundamentalsPHYSICAL IMPEDIMENTS TO TRADE CAUSE COMPETITIVE PRICES TODIFFER; THE DIFFERENCE IS THE PRICE OF CONGESTION. Power lines,because of their limited capacity, often cause energy prices to differ betweenlocations. Congestion prices were not invented for electricity grids, need not becentrally calculated, and occur on their own in competitive markets.Chapter Summary 5-3: If there are binding physical transmission limits betweendifferent locations, a competitive bilateral market with physical transmission rightswill trade power at different prices in different locations. These competitivelocational prices of power (CLPs) are unique, are the same as nodal prices (LMPsor LBMPs), and are the only efficient prices.Section 1: Congestion Pricing is Competitive Pricing. If the transmissionline between two locations is inadequate to handle the desired trade between thosetwo locations, the downstream location will be forced to buy power from moreexpensive local generators, This will raise the local price of power relative to theremote price, which is a standard competitive result and has nothing to do withcentralized computation.Section 2: Benefits of Competitive Locational Pricing. Like all competitiveprices, CLPs minimize the cost of production and reveal to consumers the true costof their consumption. CLPs at each location equal the systems marginal cost ofproviding power at that location.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Investigations . . . indicated such great simplification in wireless telephoneapparatus that wemay, within thequitenear future, haveplaced at our disposal a simpleportableapparatus whichwill permit wireless conversation to becarried on over a considerablearea. This will proveofgreat valuein sparsely settled districts.George Westinghouse1911Chapter 5-4Congestion Pricing MethodsTHE POINT OF CENTRAL CALCULATION IS TO FIND THE PERFECTLYCOMPETITIVE, BILATERAL-MARKET PRICES. If competition is strong in acentralized market, bids will be honest and the data used in the central computationaccurate. Though bilateralists often object to nodal or marginal-cost locationalprices, bilateral theorists know that theoretical nodal prices are exactly the pricesa bilateral market would produce if it worked perfectly. The real debate is not overthe prices but over which system will do a better job of finding them.Chapter Summary 5-4: Central computation finds the optimal dispatch andthen computes prices from the marginal benefits of a free megawatt at each location.Transmission constraints make power more valuable in some locations than others.Bilateral traders never consider the optimal dispatch but look only for profitabletrades. Arbitrage produces a single price at each location, but transmission con-straints can prevent it from leveling prices between locations. These two differentprocesses lead to the same quantities being traded and to the same prices becauseperfectly competitive bilateral trade is efficient.Section 1: Centralized Computation of CLPs. Central computation of CLPsmakes the ISO the trading partner of every buyer and seller and does not pricecongestion separately. Power flows in a looped network are governed by theimpedances (resistances) of the lines. This is illustrated with a three-line loopednetwork with one constrained line. If the constraint is binding, all three buses willhave different prices, and these will cause generators to minimize the total costof production.Section 2: Comparing Bilateral and Central Congestion Pricing. Competi-tive bilateral trading produces the same locational prices in the example networkas central computation. The bilateral system collects congestion rent by sellingFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Furthermore, theuseof electricity will conservethecoal deposits of theworld. George Westinghouse1911Chapter 5-5Congestion Pricing FallaciesNOT REALIZING THAT CONGESTION PRICING IS COMPETITIVE PRIC-ING, ADVOCATES OF COMPETITION CRITICIZE IT AS UNFAIR. Competitivelocational prices, like all competitive prices, contain scarcity rents that cover fixedcosts of generators as well as congestion rents that cover the fixed costs of the grid.None of this revenue is wasted, and occasional high prices caused by congestionsend the right signals to investors to build new generators, to customers to use lesspower, and to the ISO to build needed lines.Section 1: Are Competitive Locational Prices Too High? Congestion ismanaged by redispatching expensive local generation in place of cheaper remotegeneration. Usually the additional production cost is much less than the cost toconsumers, and this is often cited as a failure of competitive locational pricing.The high prices are necessary, however, to cover the fixed costs of an efficient setof generators and to cover fixed transmission costs.Section 2: Congestion Taxing. Critics of congestion pricing usually suggestcongestion taxing, instead of congestion pricing, though not by that name. Thisthree-step plan first pretends congestion does not exist and finds a single price toclear the entire market. Then the ISO redispatches around the congestion, at a cost,and finally taxes consumers to pay the redispatch cost. If generators would bidhonestly, the tax would be small, but the system induces dishonest bidding thatresults in a higher average price for power than does standard congestion pricing.5-5.1 ARE COMPETITIVE LOCATIONAL PRICES TOO HIGH?Fallacies of congestion pricing tend to focus on the occasional high prices causedby local scarcity when import lines are congested. Perhaps the most articulateexposition of these misconceptions is found in Rosenberg (2000).February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.When asked by Gladstoneif electricity would haveany practical value, Faraday replied,Why sir, thereis every possibility that you will soon beableto tax it.Michael FaradayChapter 5-6Refunds and TaxesHOW SHOULD THE ISO REFUND CONGESTION RENT AND COLLECTREVENUE SHORTFALLS? The answer is surprisingly simple. Over- and under-collections of revenue should be added together and collected as a flat energy chargeor tax. Whether to collect it from generators or loads should be decided as matterof convenience as the tax incidence of both choices is the same.This answer depends on defining prices as charges intended to allocateresources efficiently and taxes as charges intended to raise revenue. The answeris most convincing if prices have been designed as efficiently as possible. Somewill argue that because prices are not yet right, taxes should be designed to compen-sate for their shortcomings. But if taxes begin to take on the role of prices, improvedprices will then be disputed on the basis that these would interfere with the incen-tives of the tax structure. The best designs will result from separating the two tasks:taxes should only raise revenue to pay for fixed-costs of the system, while pricesshould be designed with only efficiency in mind.Chapter Summary 5-6: Pricing should be used to the greatest practical extentfor two reasons: (1) to maximize efficiency, and (2) to minimize taxes. Taxes shouldbe designed to minimize deadweight loss. This is accomplished easily with a flatcharge on energy.Section 1: Pricing versus Taxing. System prices are defined as chargesintended to increase efficiency, while system taxes are defined as charges intendedto raise revenue. As many services and externalities as possible should be pricedefficiently, both to raise revenue and to increase efficiency. The inevitable revenueshortfall must be recovered through taxes which should be designed to reduceefficiency as little as possible. A flat energy tax does this so well there is littlechance for improvement.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Reason and Justicetell methat thereis moreloveof man in electricity and steam, than inchastity and refusal to eat meat. Anton Chekhovletter, concerning Tolstoy1894Chapter 5-7Pricing Losses on LinesLOSSES ARE MORE THAN THE SUM OF THEIR PARTS. If one power flowloses 10 MW to heating power lines and another loses 20 MW, the two flowstogether will lose 58.3 MW. Billing for the extra 28.3 MW of losses has causedmuch controversy. To make matters worse, economists suggest charging the firstpower flow the cost of replacing 38.9 MW and the second the cost of replacing77.7 MW. Together this is double the actual cost of losses.Though charging transmission users for marginal losses often seems unfair tothose being charged, it is what a competitive market in transmission would do. Asalways, the competitive approach increases market efficiency relative to theregulatory average-cost approach. The fact that it causes an overcollection is alsoan advantage as the revenue can be used to reduce the inefficient taxes that areneeded to cover various fixed costs (see Chapter 5-6).Chapter Summary 5-7: If transmission were provided by many small competingline owners, each with an unconstrained line, the price of transmission would equalthe marginal cost of losses. This price would minimize the total cost of power.Section 1: The Competitive Price Is Twice the Average Cost. Marginal-costpricing means charging a power flow for the losses caused by a 1-MW increaseof the flow times the amount of the flow. It collects about twice the cost of replacingtotal losses.Section 2: Competitive Loss Pricing. A decentralized (bilateral) competitivetransmission market would price losses at marginal cost thereby collecting aboutdouble the cost of the losses.Section 3: Inefficiency of Average-Loss Pricing. Average-cost pricing oflosses causes an inefficient dispatch and thereby increases the total cost of power.When generation is not otherwise constrained, the cost increase is approximatelyequal to the total cost of losses under an efficient dispatch.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Her own mother lived thelatter years of her lifein thehorriblesuspicion that electricity wasdripping invisibly all over thehouse. James ThurberMy Lifeand Hard Times1933Chapter 5-8Pricing Losses at NodesLOSS PRICING, LIKE CONGESTION PRICING, CAN BE SIMPLIFIED BYUSING NODAL PRICES. By charging each generator and load the loss price atits bus, all trades will be charged properly for their losses. Also, if politics preventslocational pricing for loads, generators will still receive correct price signals.It is easiest to charge for losses by including loss prices in the competitivelocational prices (CLPs), but if they are charged separately and billed after the fact,generators will learn to adjust their bids and the market will still handle losses quiteefficiently. Even the restrictions that total loss charges not exceed the value of lostpower and that losses be paid for in kind can be handled quite efficiently by shiftingnodal loss prices.Chapter Summary 5-8: By choosing a reference bus, marginal loss prices canbe computed at every bus. These are relative prices, but that is all that is needed.If losses are not collected from loads, then the total collection of losses can becontrolled by choosing the reference bus. One nearer to load increases collections,and one nearer to generation decreases it. Shifting the reference bus shifts all lossprices uniformly, which has no economic impact for reasons discussed in Chapter5-6. In particular, loss charges can be adjusted so that generators pay marginal lossprices, but total collections equal the total cost of loss replacement.Section 1: Nodal Loss Prices. Unlike bilateral loss prices, which have anabsolute value, nodal prices are relative. System physics cannot attribute lossesto a power injection but only to a point-to-point power transfer. Similarly, onlythe differences between nodal loss prices are meaningful. Choosing a reference or swing bus allows both losses and loss prices to becomputed on a nodal basis, but both give absolute answers only when used in pairscorresponding to an injection and a withdrawal.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. This is not the contract-path fiction. It accounts for paths but not for counterflow cancellations.Today's scientific question is: What in theworld is electricity and wheredoes it go after it leaves thetoaster?Dave BarryChapter 5-9Transmission RightsFINANCIAL RIGHTS REFLECT ELECTRICAL REALITY; PHYSICALRIGHTS REFLECT AN ILLUSIONTHE NOTION THAT SUPPLIERS ACTU-ALLY DELIVER THEIR PRODUCT TO THEIR CUSTOMERS.1 If supplier A sendspower to load B and supplier B sends power to load A, their shipments may physi-cally cancel each other on the connecting power line with the result that no powerflows from A to B or from B to A. Instead supplier As power goes to supplier Bscustomer and vice versa.Suppose that instead of selling in their own regions, the Northern Californiagenerators decide to sell to Southern California and vice versa. Nothing physicalchanges. The same generators produce, the same loads consume, and the sameamounts of power flow over the same paths. But with the new contracts, traderswish to own 10 GW of north-south rights and 10 GW of south-north rights. If therights are financial, they just cancel out for the issuer. Whatever they pay to oneset of rights they collect fromthe other. This calculation so perfectly mirrors physicsthat when financial rights are summed to find out if the total set is feasible, theyare first converted to power flows and then summed by the engineers.Issuing 10 GW of physical rights in each direction is next to impossible. Thephysical path may be limited to 2 GW. What if 4 GW of south-north rights werenot exercised? The path would be burned out if the 10 GW of north-south rightswere exercised, so 2 GW of north-south flow would be cancelled. Such rights arenot very firm. To ensure that physical rights are firm, the issuance of such rightsis limited to 2 GW in each direction on a 2 GW path. This forces trade to fit thelimited concept of goods moving from supplier to customer without the possibilityof automatic rerouting according to the far more efficient laws of power flow.Financial rights automatically cancel and reroute just as do power flows.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Power SystemEconomicsDesigning Markets for ElectricityS t e v e n S t o f tIEEE / WileyFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Cover painting by W. Louis Sonntag, J r. (1869-1898), The Bowery atNight, c. 1895. Early deregulated electricity market with trolleys poweredby Westinghouses AC and shops probably illuminated with Edisons DC.The houses may still be lit by gas. The Third Avenue Elevated (1878),whose noise and shadows contributed to the decline of New Yorks once-elegant theater district, will soon be electrified. (Uncle Toms Cabin wasfirst staged in the Bowery Theatre visible at the extreme left.) Arc lights,brought to New York streets in 1880 by Charles Brush, transformed nightlife. Sonntag frequently depicted the resulting sense of glamour and ex-citement. The watercolor was a Gift of Mrs. William B. Miles to the Mu-seum of the City of New York.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.For my mother, whose writing inspired me to think I could,and my father who taught me to test high voltage with one hand behind my backFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Contents in BriefList of Results and Fallacies xivPreface xviiiAcronyms and Abbreviations xxSymbols xxiiPart 1. Power Market FundamentalsPrologue 2Why Deregulate? 6What to Deregulate 17Pricing Power, Energy, and Capacity 30Power Supply and Demand 40What Is Competition? 49Marginal Cost in a Power Market 60Market Structure 74Market Architecture 82Designing and Testing Market Rules 93Part 2. Reliability, Price Spikes and InvestmentReliability and Investment Policy 108Price Spikes Recover Fixed Costs 120Reliability and Generation 133Limiting the Price Spikes 140Value-of-Lost-Load Pricing 154Operating-Reserve Pricing 165Market Dynamics and the Profit Function 174Requirements for Installed Capacity 180Inter-System Competition for Reliability 188Unsolved Problems 194Part 3. Market ArchitectureIntroduction 202The Two-Settlement System 208Day-Ahead Market Designs 217Ancillary Services 232The Day-Ahead Market in Theory 243The Real-Time Market in Theory 254The Day-Ahead Market in Practice 264The Real-Time Market in Practice 272The New Unit-Commitment Problem 289The Market for Operating Reserves 306Part 4. Market PowerDefining Market Power 316Exercising Market Power 329Modeling Market Power 337Designing to Reduce Market Power 345Predicting Market Power 356Monitoring Market Power 365Part 5. Locational PricingPower Transmission and Losses 374Physical Transmission Limits 382Congestion Pricing Fundamentals 389Congestion Pricing Methods 395Congestion Pricing Fallacies 404Refunds and Taxes 411Pricing Losses on Lines 417Pricing Losses at Nodes 424Transmission Rights 431Glossary 443References 455Index 460February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.ContentsList of Results and Fallacies xivPreface xviiiAcronyms and Abbreviations xxSymbols xxiiPart 1. Power Market Fundamentals Prologue 2Reading to Different Depths 3Reading Out of Order 41-1 Why Deregulate? 6Conditions for Deregulation 9Problems with Regulation 10The Benefits of Competitive Wholesale Markets 12The Benefits of Real-time Rates 13Problems with Deregulating Electricity 141-2 What to Deregulate 17Ancillary Services and the System Operator 19Unit Commitment and Congestion Management 22Risk Management and Forward Markets 25Transmission and Distribution 25Retail Competition 261-3 Pricing Power, Energy, and Capacity 30Measuring Power and Energy 32Measuring Generation Capacity 33Pricing Generation Capacity 33Technical Supplement 391-4 Power Supply and Demand 40Describing the Demand for Power 41Screening Curves and Long-Run Equilibrium 44Frequency, Voltage, and Clearing the Market 45February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Contents ix1-5 What Is Competition? 49Competition Means More than Struggle 51The Efficiency of Perfect Competition 52 Short- and Long-Run Equilibrium Dynamics 56Why Is Competition Good For Consumers? 591-6 Marginal Cost in a Power Market 60The Role of Marginal Cost 62Marginal-Cost Fallacies 63The Definition of Marginal Cost 65Marginal Cost Results 67Working with Marginal Costs 69Scarcity Rent 701-7 Market Structure 74Reliability Requirements 76Transmission 77Effective Demand Elasticity 78Long-Term Contracts 80Supply Concentration 801-8 Market Architecture 82Listing the Submarkets 84Market Types: Bilateral through Pools 86Market Linkages 891-9 Designing and Testing Market Rules 93Design for Competitive Prices 95Design to Prevent Gaming 98Auctions 99Testing a Market Design 101Technical Supplement: Example of a Bottom-Line Test 103Part 2. Reliability, Price Spikes, and Investment 2-1 Reliability and Investment Policy 108Price Regulation is Essential 111The Profit Function 114Side Effects of Reliability Policy 116Inter-System Competition 117Demand-Side Effects of Price Limits 1182-2 Price Spikes Recover Fixed Costs 120The Fixed-Cost Fallacy 121Optimal Price Spikes for Peakers 123The Lumpiness of Fixed Costs 129February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.x Contents2-3 Reliability and Generation 133Operating Reserves and Contingencies 134Adequacy and Security 135The Simple Model of Reliability 136The Fundamental Reliability Question 1392-4 Limiting the Price Spikes 140Normal Market Operation with Limited Demand Elasticity 142Market Failure with a steep load-duration curve 144Suppressing the Balancing Market to Avoid Regulating Price 145Setting Price to the Last Clearing Price 148How Real-Time Price Setting Caps the Forward Markets 150Technical Supplement: The Condition for Failure 1522-5 Value-of-Lost-Load Pricing 154Valuing Lost Load 155VOLL Pricing is Optimal in the Simple Model of Reliability 157Practical Considerations 159Technical Supplement 1632-6 Operating-Reserve Pricing 165Less Risk, Less Market Power 166How Can OpRes Pricing Be Better than Optimal? 1722-7 Market Dynamics and the Profit Function 174Calculating Profit Functions 175Interpreting the Profit Function 1772-8 Requirements for Installed Capacity 180The Capacity-Requirement Approach 181Short-Run Profits with a Capacity Requirement 182Combining a Capacity Requirement with a Price Spike 184Comparing the Two Approaches 1862-9 Inter-System Competition for Reliability 188Price-Cap Competition 189Competition between Price Spikes and Capacity Requirements 1912-10 Unsolved Problems 194High Marginal Costs and Low Price Caps 195Pricing Supply and Demand Separately 197Price-Elastic Demand for Operating Reserves 197The Psychology of System-Operators 198Part 3. Market Architecture 3-1 Introduction 202Spot Markets, Forward Markets and Settlements 203Architectural Controversies 204Simplified Locational Pricing 206February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Contents xi3-2 The Two-Settlement System 208The Two-Settlement System 209Ex-Post Prices: The Traders Complaint 2143-3 Day-Ahead Market Designs 217How Day-Ahead Auctions Determine Quantity and Price 218Summaries of Four Day-Ahead Markets 223Overview of the Day-Ahead Design Controversy 2303-4 Ancillary Services 232The List of Ancillary Services 233Real-Power Balancing and Frequency Stability 236Voltage Stability for Customers 238Transmission Security 238Economic Dispatch 240Trade Enforcement 2403-5 The Day-Ahead Market in Theory 243Equilibrium Without a Clearing Price 244Difficulties with Bilateral Day-Ahead Markets 247Settlement, Hedging, and Reliability 250Other Design Considerations 2523-6 The Real-Time Market in Theory 254Which Trades Are Part of the Real-Time Market? 255Equilibrium Without a Market-Clearing Price 258Why Real-Time Markets Are Not Purely Bilateral 2613-7 The Day-Ahead Market in Practice 264Arbitrage vs. Computation 265Efficiency 268Reliability and Control 269Risk Management 2703-8 The Real-Time Market in Practice 272Two Approaches to Balancing-Market Design 274The Marginal-Cost Question As Decided by FERC 277Making Sense of the Marginal-Cost Pricing Charade 279The Power Exchange Approach 2853-9 The New Unit-Commitment Problem 289How Big Is the Unit-commitment problem? 291Unit Commitment in a Power Exchange 294Investment Under a Power Pool 3023-10 The Market for Operating Reserves 306Types of Operating Reserve 307Scoring by Expected Cost 309Scoring Based on the Capacity Bid Only 310Opportunity-Cost Pricing 313February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.xii ContentsPart 4. Market Power 4-1 Defining Market Power 316Defining Market Power 318Defining Price-Quantity Outcomes 319Three Stages of Market Power 321Using Price-Quantity Outcomes to Show Market Power 323Monopoly Power in a Power Auction 326Market Power on the Demand Side 3274-2 Exercising Market Power 329Market Power and Forward Markets 330Long-Run Reactions to Market Power 331Marginal and Nonmarginal Generators 332The Two Effects of Market Power 333Long-Run and Short-Run Market Power 334Is a 1000% Markup Too Much? 3364-3 Modeling Market Power 337Monopoly and the Lerner Index 338The Cournot Model 340Unilateral Action and the HHI 342Technical Supplement: Markup Determination 3434-4 Designing to Reduce Market Power 345Demand Elasticity and Supplier Concentration 346What Keeps Prices Down? 347Forward Contracts and Obligations 347Demand Uncertainty and Supply-Curve Bidding 351Technical Supplement: Calculations for Section 4-4.3 3534-5 Predicting Market Power 356Four Factors that HHI Ignores 357Why the Lerner Index Is Unreliable 358Estimating Market Power 361Technical Supplement: Market Power and Forward Contracts 3634-6 Monitoring Market Power 365FERCs Ambiguous Standard 366Market Monitoring 368Part 5. Locational Pricing 5-1 Power Transmission and Losses 374DC Power Lines 375AC Power Lines 3785-2 Physical Transmission Limits 382Thermal Limits on Power Lines 383Reactive Power and Thermal Limits 384Stability Limits on Power Lines 386February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Contents xiii5-3 Congestion Pricing Fundamentals 389Congestion Pricing Is Competitive Pricing 390Benefits of Competitive Locational Prices 3935-4 Congestion Pricing Methods 395Centralized Computation of CLPs 396Bilateral Pricing Compared to Centralized Pricing 3995-5 Congestion Pricing Fallacies 404Are Competitive Locational Prices Too High? 404Congestion Taxing 4085-6 Refunds and Taxes 411Pricing Versus Taxing 412Energy Taxes 4145-7 Pricing Losses on Lines 417The Competitive Price is Twice the Average Cost 418Competitive Losses Pricing 419Inefficiency of Average-Cost Loss Pricing 4215-8 Pricing Losses at Nodes 424Nodal Loss Prices 425Full Nodal Pricing: Loss, Congestion and Reference Prices 427Three Common Restrictions on Losses Pricing 4295-9 Transmission Rights 431The Purpose of Transmission Rights 432Using Financial Transmission Rights 435Revenues from System-Issued Financial Rights 437Physical Transmission Rights 440Glossary 443References 455Index 460February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.List of Results and Fallacies1 11 1 The Efficient-Competition Result 10 10 10 10 The Price-Cap Result2 22 2 The Marginal-Cost Pricing Result 11 11 11 11 The Contracts-for-Differences Result 13 33 3 The Marginal-Cost Fallacy 12 12 12 12 The Contracts-for-Differences Result 24 44 4 The Ambiguous-Price Fallacy 13 13 13 13 The Efficient-Auction Result5 55 5 The System-Marginal-Cost Pricing Result 14 14 14 14 The HHI Result6 66 6 The Fixed-Cost Fallacy 15 15 15 15 The Market-Power Fallacy7 77 7 The Weak Fixed-Cost Fallacy 16 16 16 16 Locational-Pricing Result 18 88 8 The Reliability Fallacy 17 17 17 17 Locational-Pricing Result 29 99 9 The Regulatory-Price-Spike Result 18 18 18 18 The Locational-Pricing FallacyPart 1. Power Market FundamentalsWhy Deregulate?Result 1-1.1 Savings fromReal-Time Rates Would Be Small 14Pricing Power, Energy, and CapacityFallacy Fallacy Fallacy Fallacy 1-3.1 Fixed and Variable Costs Are Measured in Different Units 34Result 1-3.2 Energy, Power, and Capacity Are Priced in $/MWh 36Power Supply and DemandResult 1-4.1 Supply Equals Consumption but May Not Equal Demand 48What Is Competition?1 11 1 Result 1-5.1 Competitive Prices Are Short- and Long-Run Efficient 542 22 2 Result 1-5.2 Competitive Suppliers Set Output So That MC =P 57Result 1-5.3a Under Competition, Average Economic Profit Is Zero 58Result 1-5.3b Under Competition, Fixed Costs Are Covered 58Result 1-5.3c A Supplier with a Unique Advantage Can Do Better 58Marginal Cost in a Power Market3 33 3 Fallacy Fallacy Fallacy Fallacy 1-6.1 Marginal Cost Equals the Cost of the Last Unit Produced 644 44 4 Fallacy Fallacy Fallacy Fallacy 1-6.2 When Marginal Cost Is Ambiguous, so Is the Competitive Price 65Result 1-6.1 Competitive Suppliers Set Output so MCLH<

P <

MCRH5 55 5 Result 1-6.2 Competitive Price Equals SystemMarginal Cost 68Result 1-6.3 Supply Intersects Demand at the Competitive Price 69Market ArchitectureResult 1-8.1 The Forward Price Is the Expected Future Spot Price 90Designing and Testing Market RulesFallacy Fallacy Fallacy Fallacy 1-9.1 Scarcity Rents Are Unfair 95Result 1-9.1 Changing the Markets Rules Changes Behavior 97Result 1-9.2 Design Market Mechanisms to Induce Truth Telling 99Result 1-9.3 Four Types of Auctions Produce the Same Revenue 100Result 1-9.4 A Vickrey Auction Is Incentive Compatible 100February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.List of Results and Fallacies xvPart 2. Reliability, Price Spikes, and InvestmentPrice Spikes Recover Fixed Costs6 66 6 Fallacy Fallacy Fallacy Fallacy 2-2.1 Marginal-Cost Prices Will Not Cover Fixed Cost 121Result 2-2.1 In the Long-Run, Suppliers Recover Their Fixed Costs 123Result 2-2.2 Long-Run EquilibriumConditions for Two Technologies 1287 77 7 Fallacy Fallacy Fallacy Fallacy 2-2.2 Marginal-Cost Pricing Causes a Capacity Shortage 129Result 2-2.3 Marginal-Cost Prices Induce the Optimal Mix of Technologies 129Result 2-2.4 Inefficiency Caused by the Lumpiness of Generators Is Negligible 131Reliability and GenerationResult 2-3.1 Optimal Duration of Load Shedding Is D*LS=FCpeak'VLL139Limiting the Systems PriceResult 2-4.1 A Small Amount of Elastic Demand Can Make the Market Efficient 143Result 2-4.2 Too Little Demand Elasticity Can Cause the Real-Time Market to Fail 145Result 2-4.3 Suppressing the SystemOperators Balancing Market Is Inefficient 1478 88 8 Fallacy Fallacy Fallacy Fallacy 2-4.1 The Market Will Provide Adequate Reliability 111, 1479 99 9 Result 2-4.4 Regulatory Policy Determines the Height and Duration of Price Spikes 114, 147Result 2-4.5 Do Not Cap Prices at the Highest Demand Bid 15010 10 10 10 Result 2-4.6 The Real-Time Price Limit Effectively Caps the Entire Market 113, 152Result 2-4.7 Conditions for the Failure of a Power Market 152Result 2-4.8 Conditions for an Efficient Power Market 153Value-of-Lost-Load PricingFallacy Fallacy Fallacy Fallacy 2-5.1 VOLL Cannot Be Usefully Defined 156Result 2-5.1 Within the Simple Model of Reliability, VOLL Pricing Is Optimal 159Result 2-5.2 Inaccuracy of Estimation Does Not Rule Out the Use of VOLL 159Fallacy Fallacy Fallacy Fallacy 2-5.2 Risk fromVOLL Pricing Is Beneficial 161Operating-Reserve PricingResult 2-6.1 Many Different Price Limits Can Induce Optimal Investment 116, 168Result 2-6.2 A Lower, Longer-Duration Aggregate Price Spike Is Less Risky 169Result 2-6.3 High Price Caps Invite the Exercise of Market Power 171Result 2-6.4 Reliability Policy Should Consider Risk and Market Power 117, 173Market Dynamics and the Profit FunctionResult 2-7.1 The Higher the Price Spikes, the Steeper the Profit Function 177Result 2-7.2 Steeper Profit Functions Increase Risk and Market Power 178Requirements for Installed CapacityResult 2-8.1 Energy and Capacity Prices Together Induce Investment 115, 181Result 2-8.2 A Capacity Requirement Can Eliminate the Need for Price Spikes 184Result 2-8.3 VOLL Pricing Induces Optimal ICap Even When ICap Is Random 185Result 2-8.4 Profit Functions Are Additive, But Resulting Profits Are Not 186Inter-System Competition for ReliabilityResult 2-9.1 Competition Between SystemOperators Induces High Price Spikes 118, 190Result 2-9.2 Trading between Markets with Different Policies Can Reduce Reliability 191Result 2-9.3 Capacity-Requirement Markets Need Annual Requirements 192Unsolved ProblemsResult 2-10.1 The Price of Operating Reserves Should Increase When They Are Scarce 198February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.xvi List of Results and FallaciesPart 3. Market ArchitectureThe Two-Settlement SystemResult 3-2.1 A Two-Settlement SystemPreserves Real-Time Incentives 21011 11 11 11 Result 3-2.2 A Contract for Differences Insulates Traders fromSpot Price Volatility 21212 12 12 12 Result 3-2.2 Contracts for Differences Preserve Real-Time Incentives 213Day-Ahead Market Designs13 13 13 13 Result 3-3.1 A Single-Price Day-Ahead Auction Is Efficient 220Ancillary ServicesResult 3-4.1 Strictly Bilateral Power Trading Requires Centralized Coordination 241The Day-Ahead Market in TheoryResult 3-5.1 A Bilateral DA Market Decreases Reliability 249Result 3-5.2 Side-Payments in a Day-Ahead Pool Do Not Increase Reliability 252The Real-Time Market in TheoryResult 3-6.1 Real-Time Power Is Not Bought or Sold Under Contract 256Result 3-6.2 Real-Time Pools Sometimes Require Direct Control of Generation 259The Day-Ahead Market in PracticeResult 3-7.1 A Day-Ahead Power Pool Is Not Required for Reliability 269The Real-Time Market in PracticeResult 3-8.1 SMC Unit Commitment with Elastic Demand Is Inefficient 283Result 3-8.2 System-Marginal-Value Pricing Provides Efficient Demand Incentives 284The New Unit-Commitment ProblemResult 3-9.1 A Power Exchanges Unit-Commitment Inefficiency Is Less Than 1%. 293Result 3-9.2 Marginal Cost Prices Can Solve Some Unit-Commitment Problems 294Result 3-9.3 A Power Exchange Lacks a Classic Competitive Equilibrium 297Result 3-9.4 A Power Pool with Accurate Bids Induces the Optimal Dispatch 297Result 3-9.5 Two-Part Bids Can Solve Some Unit-Commitment Problems 298Result 3-9.6 A Power Exchange Has a Nearly-Efficient Nash Equilibrium 300Result 3-9.7 Side Payments in Power Pools Distort Investment in Generation 303The Market for Operating ReservesResult 3-10.1 Capacity-Bid Scoring for Spinning Reserves Is OptimalPart 4. Market PowerDefining Market PowerResult 4-1.1 Monopoly Power Always Causes the Quantity Withheld to be Positive 325Result 4-1.2 When Assessing Monopoly Power, Ignore Demand-Side Flaws 325Result 4-1.3 Profitably Raising the Market Price May Not Be Market Power 326Exercising Market PowerResult 4-2.1 Market Power Cannot Be Exercised in Day-Ahead Power Markets 331Result 4-2.2 The Bid that Raises the Price May Not Set the Price 332Modeling Market Power14 14 14 14 Result 4-3.1 The Average Lerner Index Equals HHI Over Demand Elasticity 342Predicting Market PowerResult 4-5.1 Price Distortion Measures Market Power Better 361Monitoring Market Power15 15 15 15 Fallacy Fallacy Fallacy Fallacy 4-6.1 Some Market Power Is Needed and Beneficial 370Fallacy Fallacy Fallacy Fallacy 4-6.2 Market Power Cannot Be Proven 370February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.List of Results and Fallacies xviiPart 5. Basic Locational PricingPower Transmission and LossesResult 5-1.1 Kirchhoffs Laws 376Result 5-1.2 Power Equals Voltage Times Current (Volts Amps) 377Result 5-1.3 Ohms Law Is Voltage Equals Current Times Resistance (I R) 377Result 5-1.4 Transmission Losses Are Proportional to Power2 / Voltage2 378Physical Transmission LimitsResult 5-2.1 Thermal Limits Depend on Real and Reactive Power Flows 385Congestion Pricing FundamentalsResult 5-3.1 Transmission Price AB Is the Power Price Difference, PB !! PA39216 16 16 16 Result 5-3.2 Only Competitive Locational Prices Minimize Total Production Cost 394Congestion Pricing MethodsResult 5-4.1 Power Flows Are Approximately Additive 39717 17 17 17 Result 5-4.2 Competitive Bilateral Prices Equal Centralized Locational Prices 401Congestion Pricing Fallacies18 18 18 18 Fallacy Fallacy Fallacy Fallacy 5-5.1 Congestion Rent >Redispatch Cost Is Unfair to Consumers 406Refunds and TaxesResult 5-6.1 Price for Efficiency and Not to Raise Revenue 414Result 5-6.2 Tax for Revenue and Not to Improve Efficiency 414Result 5-6.3 An Energy-Based Transfer fromGenerators to Loads has No Net Effect 415Result 5-6.4 An Energy Tax on Load or Generation Will Be Paid by Load 416Pricing Losses on LinesResult 5-7.1 Marginal Losses Are Twice Average Losses 418Result 5-7.2 The Competitive Charge for Transmission Is Twice the Cost of Losses 419Result 5-7.3 Competitive Bilateral Loss Prices Equal Marginal Cost 421Result 5-7.4 Average-Cost Loss Pricing Raises the Cost of Production 423Pricing Losses at NodesResult 5-8.1 Changing the Reference Bus Changes Loss Prices Uniformly 427Result 5-8.2 Changing the Reference Bus Does Not Affect Bilateral Trades 427Transmission RightsResult 5-9.1 Trading Opportunities Are Not Blocked by Congested Lines 433Result 5-9.2 Revenue froma Feasible Set of TCCs Will Be Sufficient 439Result 5-9.3 The Feasible Set of Physical Rights Cannot Account for Counterflows 440February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.PrefaceMy original purpose in writing this book was to collect and present the basiceconomics and engineering used to design power markets. My hope was to dispelmyths and provide a coherent foundation for policy discussions and market design.In the course of writing, I came to understand there is no received wisdomto presenton two key issues: price-spikes and pools. While the majority of the book still holdsto my first purpose, Parts 2 and 3 are guided as well by a second. They seek topresent the two unresolved issues coherently, answer a few basic questions andhighlight some of the gaps in our current understanding.The price-spike issue is how to design the market to accommodate two demand-side flaws underlying the price-spikes that provide incentives for investment ingeneration. Part 2 shows that some regulation is required until one flaw has beenmitigated. The first regulatory goal should be to ensure the revenue from theaggregate price spike is just sufficient to induce a reliable level of generatingcapacity. This revenue is determine by (1) the duration of the aggregate price spikewhich is under the influence of NERC guidelines and (2) the height of the pricespike which is regulated by FERC. Currently, neither institution appears aware theirpolicies jointly determine investment.Part 2 provides a framework for computing the level of investment induced byany combination of NERC and FERC policies. Because many combinations willwork, it suggests a second goal. Price volatility should be reduced to levels thatmight be expected from a mature power marketlevels far below those observedin the current markets with their incapacitated demand sides. I hope Part 2 willclarify the regulatory options and the need to fix the markets demand side.While Part 3 presents the standard principles of bilateral markets, exchangesand pools, it is able to make little progress on the second issue, the power-poolquestion. An exchange is a widely used form of centralized marketthe New YorkStock Exchange is an examplewhile pools are peculiar to power markets. Ex-changes trade at one price at any given time and location, while pools pay differentprices to different generators according to their costs. The differences in transpar-ency and operation are considerable as may be their performance. Unfortunately,little theoretical or empirical research is to be found, and Part 3 can only raise issuesand show the answers are far from obvious.While three pools operate in the eastern U.S. and PJ M has been deregulatedfor nearly four years, no evaluation of their efficiency has been undertaken. Theonly national effort, a shoestring operation at the Department of Energy, has beencrippled by lack of access to data that FERC could easily obtain from the pools.Pro-pool forces within FERC have, for years, blocked any suggestion to evaluatethe performance of pools or their potential benefits. No description of any easternFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Preface xixpool, suitable for economic analysis, can be found within FERC or in the publicdomain.Theoretical pool descriptions cover ex-ante pricing while knowledgeableobservers indicate the eastern ISOs use ex-post pricing. This is said to be basedon a philosophy of controlling quantities in real-time and computing prices afterthe fact. In practice, it involves proprietary calculations that apparently assumethe operators actions were optimal. I could discover no useful discussion of thetheory of this critical issue, so readers of Part 3 must wait for a later edition.Competitive power markets, like regulated markets, must be designed anddesigned well. Because of the poor quality of many current designs and the lackof a well-tested standard, this book does not recommend a rush to deregulate. Agiven deregulation may succeed, but economic theory cannot predict when sucha complex political process, once begun, will be out-maneuvered by the forces itseeks to harness. If a market is being designed or redesigned, this book is meantto help; if the decision is to wait, this book is meant to make the wait shorter.AcknowledgmentsThose who undertook to read, correct and criticize drafts provided an invaluableservice and deserve thanks from all of my readers, whom they have protected frommany confusions, diversions, and errors. For this difficult undertaking I am espe-cially grateful to Ross Baldick, J oe Bowring, Haru Connally, Rob Gramlich, DougHale, Alex Henney, Bill Hogan, Mat Morey, Sabine Schnittger, and Jurgen Weiss.Many others have made more narrowly focused but still invaluable contributions.They provided an ongoing discussion on many topics and constantly provided freshviews and caught errors. Thanks to Darwin Anwar, Gerry Basten, RichardBenjamin, Severin Borenstein, J ason Christian, Ed Mills, Udi Helman, MikeRothkopf, Erik Hirst, Ben Hobbs, Mangesh Hoskote, Marcelino Madrigal, DaveMead, J oshua Miller, Alan Moran, J im Kritikson, Dan Gustafson, Frank Felder,Carl Fuchshuber, Richard Green, Harry Singh, Alasdair Turner, Hugh Outhred,Gail Panagakis, Alex Papalexopolous, Gregory Werden, and J ames Wightman.Without the patient support of the IEEE/Wiley staff, J ohn Griffen, TonyVengraitis, and Andrew Prince, none of this would have been possible. My copyeditor, Susan Ingrao, has been a pleasure to work with and tremendously informa-tive, even answering arcane typesetting questions. Remaining errors are the resultof my inaccurate corrections or last minute changes.For support and guidance on every challenge, I have turned first to my wifePamela who has been my creative advisor, editor, and legal counsel. I thank herfor her abundant patience and unerring judgement.But of all those who have contributed to this book, I owe the most to my mother,Dorothy, who brought her artistry to the dull world of power economics. Throughthree complete drafts, she gently but persistently corrected and shaped, guided andpolished. While the quality of my writing still falls far short of my mothers, itdelights me to have learned, at last, a little of her art.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Acronyms and AbbreviationsAC alternating currentACE area control errorCA ISO California Independent System OperatorCFD contract for differencesCLP competitive locational priceCR capacity requirementDA day aheadDOJ Department of J usticeFERC Federal Energy Regulatory CommissionFTR financial transmission rightFTC Federal Trade CommissionGT gas turbine generatorHHI Herfindahl-Hirschman index ICap installed capacityIPP independent power producerISO independent system operatorISO-NE ISO New EnglandLBMP locational-based marginal priceLHMC left-hand marginal costLMP locational marginal priceLRMC long-run marginal costMC marginal costNERC North American Electric Reliability CouncilNYISO the New York Independent System Operator, Inc.NYSE the New York Stock ExchangeNE Nash equilibriumOpRes operating reservePJ M Pennsylvania-New-J ersey-Maryland Independent System OperatorPTR physical transmission rightRHMC right-hand marginal costRT real time (market)RTO regional transmission organizationSMC system marginal costSMV system marginal valueTR transmission rightUC unit commitmentVOLL value of lost loadFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Acronyms and Abbreviations xxiUnits Used to Measure ElectricityV volt The unit of electrical pressureA amp The unit of electrical currentW watt Power (Energy per hour)h hour TimeWh watt-hour Energyk kilo 1000. Used in kW, kWh and kV.M mega 1,000,000. Used in MW and MWh.G giga 1,000,000,000. Used in GW.T tera 1012. Used in TWh.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.SymbolsUnits Symbol Definition

average lost load

none LXLerner index$/MWh MC marginal cost$/MWh MCRrange of MC when MC is ambiguous.$/MW OC overnight cost of capitalMW OR operating reservesMW ORRrequired OR$/MWh P spot market price of energy (may not be a clearing price).$/MWh Paauction price$/MWh P1, P0day-ahead energy price, and realtime (spot) energy price. (P0=P)$/MWh PS(.), PD(.) supply bid curve, demand bid curve$/MWh Pcapprice limit on the system operator.$/MWh PCAprice of congestion at bus A$/MWh PLAprice of losses at bus A$/MWh Pmaxmaximum market-clearing price$/MWh Pspinspin market price of energy$/MWh PT1, PT0transmission price in DA market and RT market$/MWh PTspot price at future time TMW Q market quantity tradedvolt-amps Q reactive power flowMW q quantity sold by 1 supplierMW Q1, Q0energy quantity accepted in DA auction, quantity traded in real timeMW QT1, QT0transmission quantity accepted in DA auction, quantity traded in real timenone r discount rate for investment in generation (includes risk premium)$/h R revenueFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.xxiv Symbolsohms R electrical resistanceohms RTtransmission-line resistance$/h RCsystem revenue from congestion rent$/h RTCCsystem revenue from selling TCCs$/MWh MCRHright-hand marginal costnone S bid score in an auctionnone s market sharenone ss spot-market share$/MW SC startup cost$/MW SRBshort-run profit$/MWh SRB(.) the (short-run) profit function$/MWh SRBFfinal short-run profit including day-ahead and real-time paymentsyear | date T plant life in years, or a specific future time$/h TVC total variable cost.$/h V total surplus =producer +consumer surplusvolts V voltage$/MWh VC variable costs $/MWh VLLvalue of lost load.watts W power$/MWh Y penalty for violating installed capacity requirement.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Part 1Power Market FundamentalsPrologue1 Why Deregulate?2 What to Deregulate3 Pricing Power, Energy, and Capacity4 Power Supply and Demand5 What Is Competition?6 Marginal Cost in a Power Market7 Structure8 Architecture9 Designing and Testing Market RulesFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Is it a factor haveI dreamt itthat, by means of electricity, theworld of matter has becomeagreat nerve, vibrating thousands of miles in a breathless point of time? Rather, theround globeis a vast head, a brain, instinct with intelligence! Or, shall wesay, it is itself a thought, nothingbut thought, and no longer thesubstancethat wedreamed it? Nathaniel HawthorneTheHouseOf Seven Gables 1851ProloguePOWER SYSTEM ECONOMICS PROVIDES A PRACTICAL INTRODUC- TION TO POWER-MARKET DESIGN. To assist engineers, lawyers, regulators,and economists in crossing the boundaries between their fields, it provides thenecessary background in economics and engineering. While Part 1 covers basics,it provides fresh insights ranging from a streamlined method for calculations, tothe adaptation of economics to the quirks of generation models, to the distinctionbetween the market structure and market architecture.Part2 focuses on the core structure of power markets which determines the basiccharacter of supply and demand. It encompasses demand-side flaws, short-runreliability policy and the rigidities of supply. Together these determine the notoriousprice-spikes and unstable investment pattern of power markets. Because of itsfundamental nature, this analysis can proceed without reference to locational pricingor unit commitment which gives less-technical readers access to the most importantand fundamental economics of power markets.Part3 discusses the architecture of the day-ahead and real-time markets. Thisrequires the introduction and analysis of the unit-commitment problemtheproblem of starting and stopping generators economically. To avoid unnecessarycomplexity, the other primary problem of power-system economics, networkcongestion, is postponed until Part 5. This allows a clearer comparison of the threefundamental types of power trading: bilateral trading, exchange trading and pool-based trading. Part4 detours from the drive toward an increasingly detailed view of the marketto examine market power. Although best understood in the context of Parts2 andFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.PROLOGUE 33, it does not consider the implications of the network effects described in Part5.It can be read directly after Chapters 1-5 and 1-6 if desired. Part 5 begins with morethan enough power engineering to understand losses and congestion pricing whichare its central topics. The theme of Part5 is that locational loss prices and conges-tion prices are nothing more than ordinary (bilateral) competitive market prices.The problem of market design is not to invent clever new prices but to design amarket that will reliably discover the same prices economics has been suggestingsince Adam Smith. Power markets deviate fromstandard economics in two ways: the demand sidesare largely disconnected from the market and the details of supply costs violatethe assumptions of competitive economics. Part2 focuses on the demand-side flawswhich require a regulatory intervention for a few hours per year to ensure reliabilityand efficient investment. Until these flaws are sufficiently reduced they will remaina great danger to power markets that are poorly designed. Part 2, while basic,contains the most important new material in the book.While the aggregate market supply function is perfectly normal, the details ofgeneration costs violate a basic competitive assumption. Because the violationsare small relative to the size of the market, they may require only a slight adjustmentto power exchange bids. Alternatively, a complex and opaque power pool may beneeded. The contribution of Part3 is to present this problemin an accessible mannerand to highlight crucial questions that still need answers.The book tells its story largely through examples. These are highly simplifiedbut designed to capture important phenomena and display their essential natures.The key conclusions drawn from the examples are summarized in Results andFallacies which are listed after the table of contents. Result is not the best ofterms, but Fallacy has no acceptable antonym. Results are not theorems becausethey are not stated rigorously. They are rarely new; most are standard economicwisdom applied to power markets. They are simply the key points that should beunderstood in each area. The Results distill much theory that is not presented, butthe examples reveal the mechanisms at work behind the Results. Fallacies aretreated explicitly to help dispel the handful of popular misconceptions that continu-ally cause confusion.READING TO DIFFERENT DEPTHSReaders who wish to read more deeply on some subjects than on others will findall chapters organized to facilitate this. Chapters consist of the following parts:February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.4 PART 1 Power Market FundamentalsFor the Nonlinear ReaderA few terms and concepts are crucial and, depend-ing on the reader's background, frequently misunder-stood. Other terms are specific to this book. Theseare defined here for the reader who wishes to usethe book more as a reference than a text.1. Introduction (untitled)2. Chapter Summary3. Section Summaries4. Sections5. Technical Supplement (for some chapters)Use the chapter summary of 50 to 200 words to determine if a chapter covers atopic of interest and to learn its most essential points. For a complete overview ofthe chapters content, read the Section Summaries. For the importance and contextof the chapters focus, read the introduction.When reading an entire Part, the chapter and section summaries can be skipped,though they may still provide a useful orientation. The technical supplement usuallycontains more difficult mathematics but never more than easy calculus.READING OUT OF ORDERReaders with special interests may wish to read chap-ters out of order. The book may also serve as a refer-ence, with different parts used as they become rele-vant. Although each Part of the book has been writtenfor sequential reading, any of Parts 2 through 5 maybe read after Part 1. Even within Parts, chapters in-clude cross references to assist those who read onlya particular chapter. The glossary, which defines allterms set in bold, will be particularly helpful for those who have skipped previouschapters.Skipping chapters or reading them out of order is encouraged, but the readerwill need to understand the concepts discussed below. If these seem difficult, thereader is advised to begin by reading Part 1. Further clarifications and correctionscan be found at www.stoft.com.Conventions Specific to this BookThe book follows five conventions that are not customary although they deviatefrom custom only to follow conventional economics more closely or more conve-niently.Units. Fixed cost and variable cost, as well as the cost of energy, power andcapacity are all properly measured in $/MWh. Duration, though sometimes ex-pressed in hours per year, is represented in equations by a probability. These unitsmust be understood before reading the books examples. See page 31.Marginal Cost. The standard definition is used when applicable but is generalizedto cover models that use right-angle supply curves. These assume the supply curvechanges from flat to vertical with an infinitesimal change in output. In such cases,the left- and right-hand marginal costs are defined to be the cost of the last unitFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.PROLOGUE 5produced and the cost to produce the next unit. The marginal-cost range is definedas the set of values from left-hand to right-hand marginal cost. See page 65.Variable Cost. Because marginal cost is not defined at full output for a generatorwith a standard right-angle supply function, the constant marginal cost before fulloutput is called the generators variable cost. This remains defined even whenmarginal cost is not, as it is a property of the supply curve and not dependent onthe generators level of output. See page 69.Scarcity Rent. Scarcity rent is not defined in economics texts, yet it is a termcommonly used in power economics. Popular usage attempts to distinguish betweenrents earned when supply of all generation is scarce and those earned when onlysome types are scarce. This book avoids the ambiguity inherent in such definitionsby defining scarcity rent as equal to the more conventional economic term,inframarginal rent, which is the area below the market price and above the competi-tive supply curve. See page 70.Aggregate Price Spike. The aggregate price spike is defined as the upper portionof the price duration curve, specifically the region in which price is above thevariable cost of the most-expensive investment-grade peaker (not an old, inefficientpeaker). This cut-off value is well defined only in simple models, but it still providessome intuition about real markets. Revenue associated with this spike is called theprice-spike revenue and is similar to the popular meaning of scarcity rent. See page127.Conventional Terms That Are Sometimes MisinterpretedProfits. Profit is used by economists to mean long-run economic profits, andthese average zero under perfect competition. Short-run profit equals scarcity rentminus startup and no-load costs. Short-run profits cover fixed costs. See page 58.Cost Minimization. This refers to the minimization of production cost, not tothe minimization of consumer cost.Market Clearing. A market has cleared when there are neither offers to buyoutput for more than the market-clearing price nor offers to sell output for less thanthe market-clearing price. When the market has cleared, supply equals demand.The market-clearing price need not be the competitive price, an efficient price, afair price, or the price set by the system operator.Efficiency. Efficient production minimizes production cost given the output level.Efficient trade maximizes total surplus, the sum of consumer surplus and producersurplus (short-run profits). See page 53.Spot market. The spot market is only the real-time market, not the day-aheadmarket.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. See Platt (1991) for information on central station companies and Samuel Insull. The quotation (p. 86)is froma contemporary account of Insulls address. Platt describes early competition as follows: TheChicago experience of rate wars, distributor duplication, and torn-up streets presented an alternative thatwas attractive to virtually no one. For state commissions and progressives, see Rudolph & Ridley (1986).2. Smith (1995) relies on Gregg J arrell to conclude regulation was a response to the utilities' desire toprotect profits, not a consumerist response to monopoly pricing. But Knittel (1999) tests causation byutilities and consumers and finds no significant correlation between profit change and regulation aftercorrecting J arrells endogeneity problem. This result would be expected froman analysis of profit whentwo equal forces have opposite motivations with respect to its level.Thepropensity to truck, barter, and exchangeonething for another . . . is common to all men.Adam SmithTheWealth of Nations1776Chapter 1-1Why Deregulate?IN THE BEGINNING THERE WAS COMPETITIONBRUTAL AND INEFFI-CIENT. Between 1887 and 1893, twenty-four central station power companieswere established within Chicago alone. With overlapping distribution lines, competi-tion for customers was fierce and costs were high. In 1898, the same year he waselected president of the National Electric Light Association, Samuel Insull solvedthese problems by acquiring a monopoly over all central-station production inChicago. In his historic presidential address to NELA, Insull explained not onlywhy the electricity business was a natural monopoly but why it should be regu-lated and why this regulation should be at the state level, not the local level. Insullargued thatexclusive franchises should be coupled with the conditions ofpublic control, requiring all charges for services fixed by publicbodies to be based on cost plus a reasonable profit.These ideas shocked his fellow utility executives but led fairly directly to regulatorylaws passed by New York and Wisconsin in 1907 establishing the first two stateutility commissions. Reformers of the Progressive era also lent support to regulationalthough they were about equally supportive of municipal power companies.1 Theirintention, to hold down monopoly profits, was at odds with Insulls desire to keepprofits above the competitive level, but both sides agreed that competition wasinefficient and that providing electricity was a natural monopoly.2February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-1 Why Deregulate? 73. See J oskow (2000b, 16) for a similar view of the unimportance of the demise of natural monopolycharacteristics at the generation level and the importance of the expansion of the grid, and Ruff (1999)for an alternative view of the role of the grid and transmission pricing.On the scale of an isolated city, provision of electricity is a natural monopolyand requires regulation or municipal ownership, but as transmission technologydeveloped, it brought new possibilities for trade and competition. The earliestelectric companies, for instance Brushs company which lighted New YorksBroadway in 1880, integrated generation with distribution, and, in fact, sold light,not electricity. Edison initially did the same, installing the light bulbs in the homeshe lit and charging by the number of bulbs installed. Westinghouse introduced high-voltage transmission using alternating current (AC) technology to the United Statesin 1886, and by 1892 Southern California Edison was operating a 10-kV transmis-sion line 28 miles in length. This, too, was an integrated part of a full-service utility.Integrated utilities remained natural monopolies for many years while expansionof the high-voltage transmission network continued, mainly for purposes of reliabil-ity. Eventually the entire Eastern United States and Eastern Canada were unitedin a single synchronized AC power system. By operating at extremely high voltages,this system is able to move power over great distances with very little loss, oftenless than three percent in a thousand miles. Regulated, vertically integrated utilities were well established by the time thetransmission system made substantial long-distance trade possible. As a conse-quence, trade was slow to develop, but the existence of the grid made the de-integration of the electric industry a possibility.3 Generation could now be splitoff to form a separate competitive market, while the remaining parts of the utilitiesremained behind as regulated monopolies. By 1990, encouraged by a general trendtoward deregulation, the de-integration trend in electric markets was underwayin a number of countries. Today, more than a dozen semi-deregulated electricitymarkets are operating in at least ten countries, with several operating in the UnitedStates.In spite of this apparent success, many fundamental problems remain. Afterten years of operation, the British market has declared itself a failure and replacedall of its market rules. In a single year, the California market managed to cost itscustomers more than ten years of hoped-for savings. Alberta (Canada) is worriedover the results of its recent auction of generation rights that brought in much lessrevenue than planned. New York saw prices spike to over $6,000/MWh in 2000,and the New England ISO had to close its installed capacity market due to extremeproblems with market power. But initial problems do not prove deregulation isdoomed; some markets are functioning well. A closer look at fundamental argu-February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.8 PART 1 Power Market Fundamentalsments for and against deregulation may help explain why such mixed results mightbe expected.Chapter Summary 1-1: Improvements in transmission, rather than changesin generation technology, have removed the natural monopoly character of thewholesale power market in most locations. This makes possible the replacementof regulated generation monopolies with deregulated wholesale power markets.In principle these can be more efficient than the old-style regulation. In practice,California has proven bad deregulation to be worse than mediocre regulation, andEngland has demonstrated that mediocre deregulation can bring cost-savingefficiencies to a badly regulated generation monopoly.In the short run, power-market problems tend to be more dramatic than thebenefits. The problems are primarily the result of two demand-side flaws: the almostcomplete failure of customers to respond to relevant price fluctuations, and thecustomers ability to take power from the grid without a contract. As fundamentalas these are, it is possible to design a workable market around them, but it doesrequire design as well as extensive and clever regulation. Recent U.S. history hasshown that there are three impediments to such progress: politics, special interests,and overconfidence. The last is largely due to a dramatic underestimation of theproblem.Section 1: Conditions for Deregulation. Deregulation requires the marketnot be a strong natural monopoly. One view holds that small efficient gas turbineshave overturned the natural monopoly of large coal plants. Yet todays competitivesuppliers are far larger than any coal plant, so if the size of a large coal plant wereproblematic for competition, todays markets would be uncompetitive.Section 2: Problems with Regulation. Regulation can provide strong cost-minimizing incentives and can hold prices down, but it must trade off one againstthe other. Competition can do both at once. In practice, regulators hold prices downnear long-run average costs but leave cost-minimizing incentives too weak. Theresult is high costs and high prices.Section 3: The Benefits of Wholesale Competition. Competition providesfull strength cost-minimizing incentives and, at the same time, forces average pricesdown toward their minimum. It may also encourage efficient retail prices.Section 4: The Benefits of Real-time Pricing. Competition may induce real-time pricing, which will reduce consumption during periods of peak demand. Thiswill reduce the need for installed capacity and, if extensively adopted, shouldprovide a net savings of about 2% of retail price. Although this could be achievedFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-1 Why Deregulate? 94. See J oskow and Schmalensee (1983, 54) for a discussion of firm-level economies of scale.easily under regulation, competition will provide some additional incentives, buttheir consequences are still unclear.Section 5: Problems with Deregulating Electricity. Contemporary electricitymarkets have inadequate metering. Consequently it does not make sense for loadto respond to price fluctuations, and bilateral contracts cannot be physicallyenforced in real time. As a result demand can and sometimes does exceed supply,and competitive pricing is impossible at crucial times. These flaws result in highprices that must be limited, and they provide ideal conditions for the exercise ofmarket power. Electricity markets are also extremely complex and prone to prob-lems with local market power due to the inadequacies of the transmission system.1-1.1 CONDITIONS FOR DEREGULATIONScale economies make it possible for natural monopolies to produce their outputmore cheaply than a competitive market would. A 1-MW power plant is not veryefficient, and there is no way to produce power cheaply on this small a scale. A10-MW power plant can always do better. Efficiency continues to increase signifi-cantly to about the 100-MW level but ever more slowly beyond this level. It usedto increase to about 800 MW, and it was once assumed that nuclear plants wouldbe the most economical and their most efficient size would be even greater. If theseeconomies of scale continued, the cheapest way to provide California with powerwould be to build a 25,000-MW power plant and a few smaller ones to handle loadfluctuations. But a large single power plant could not support competition. Acompetitive market necessarily utilizes smaller plants and would therefore havehigher production costs. Consumers would have to pay more if a natural monopolyis forced to operate as a competitive industry with small-scale plants.Efficiency gains from the operation of multiple plants are another possiblesource of natural monopoly. Even if very large plants are not more efficient, largegenerating companies may be. A large company can hire specialists and share partsand repair crews. If multiplant efficiencies continue to large enough scales, acompetitive market would again be less efficient than a monopolist.4If a monopolist can produce power at significantly lower cost than the bestcompetitive market, then deregulation makes little sense. The lack of a naturalmonopoly is a prerequisite to successful deregulation, or at least, the condition ofnatural monopoly should hold only weakly.Did Cheap Gas Turbines End the Natural Monopoly?One popular argument for deregulation claims technical progress has recentlynullified the conditions for a natural monopoly in generation. This view assumesgeneration had previously been a natural monopoly because the most efficient sizeFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.10 PART 1 Power Market Fundamentalspower plant was approaching 1000 MW, and new technologies have made 100-MWplants almost as efficient.If this argument were correct, then an 1000-MW supplier must in some sensebe a monopolist, and the market must need suppliers that have capacities smallerthan 1000 MW to be competitive. But in this case, deregulation must certainly havefailed in the United States because every market contains suppliers with capacitiesexceeding 1000 MW. Yet no one who suggests small efficient plants are a necessarycondition for competition seems worried by the presence of huge suppliers in thenew markets.The beliefs that the most efficient size power plant must be quite small, andthat competitive suppliers can own many such plants are contradictory. Most likelythe former is incorrect, at least in markets with peak loads of over 5000 MW.Fortunately, vast transmission grids have made such large markets the norm. Whensmall efficient plants are necessary for competition, suppliers with total generatingcapacity greater than the most efficient size plant should be prohibited. Greaterthreats of natural monopoly conditions come from the economies of multiplantcompanies and weaknesses in the power grid that effectively isolate load pocketsduring peak load conditions.1-1.2 PROBLEMS WITH REGULATIONThe most common argument for deregulation is the inefficiency of regulation. Therecan be no quarrel about its inefficiency, but it does not follow that deregulationwill be better. Deregulation is not equivalent to perfect competition which is wellknown to be efficient. Electricity markets have their own inefficiencies that needto be compared with the inefficiencies of regulation.To date, such comparisons have been largely speculative. The most decisiveanswers inevitably are based on the least information. One side claims regulationis essential because electricity is a basic need. What about housing? That need iseven more basic, and housing is 99% deregulated. The other side claims competitionprovides incentives to reduce costs, while regulation does not. What about the manyregulated utilities that have provided reliable power for many years for less than6/kWh? Do they lack all cost-minimizing incentives?One argument posits that when a regulated utility makes a bad investment,ratepayers pick up the tab; but, when an unregulated supplier makes a bad invest-ment, stockholders pick up the tab. This analysis is myopic. Particular losses fallon the stockholders of particular companies, but the cost of capital takes intoaccount the probability of such mistakes, and every mistake increases the estimatedprobability. Like all costs, the cost of capital is paid for by consumers. Not onlydoes the cost of capital average in the cost of mistakes, it also adds a risk premium.To the extent stockholders of regulated utilities are sheltered, they demand lessof a risk premium than do stockholders of unregulated suppliers. With competition,there may be fewer mistakes, but the mistakes will be paid for by consumers, anda risk premium will be added.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-1 Why Deregulate? 115. Suppliers having better information than the regulators is at the root of the regulatory trade-off problemwhich, though fundamental, is too complex to discuss here.6. In reality, cost-of-service regulation does provide incentives in two ways: regulatory lag (see J oskow2000b) which is discussed shortly, and the threat of disallowed costs.7. For instance, yardstick regulation compares the performance of one regulated firmwith other similarfirms, thus giving the regulator some of the benefit of the other firms knowledge without requiring theregulator to know details (see Tirole 1997).Regulation has two fundamental problems: (1) it cannot provide a strongincentive to suppliers as cheaply as can a competitive market, and (2) regulatorybodies themselves do not have proper incentives. Well-trained regulators couldprovide much better regulation. But for government to provide competent regula-tion, the political process would need to change. The first problem, that of incentivesprovided by regulators, is more susceptible to analysis.The Regulators DilemmaTruly competitive markets do two things at once; they provide full-poweredincentives (1) to hold price down to marginal cost, and (2) to minimize cost.Regulation can do one or the other but not both. It must always make a trade-offbecause suppliers always know the market better than the regulators.5

This trade-off is the core idea of modern regulatory theory. Perfect cost-of-service (COS) regulation is at one extreme of the regulatory spectrum. It assuresthat, no matter what, suppliers will recover all of their costs but no more. Thisincludes a normal rate of return on their investment. Perfect COS regulation holdsprices down to long-run costs but takes away all incentive to minimize cost.6 Ifthe suppliers make an innovation that saves a dollar of production costs, theregulator takes it away and gives it to the customer.At the other extreme is perfect price-cap regulation. It sets a cap on the suppliersprice according to some formula that takes account of inflation and technicalprogress, and it never changes the formula. Now every dollar saved is kept by thesupplier, so its incentives are just as good as in a competitive market. But itsdifficult to pick a price-cap formula that can be fixed for twenty years at a time.A perfect (very-long-term) price cap must always allow prices that are well abovelong-run cost to avoid accidentally bankrupting suppliers. Consequently, priceswill be too high.The reader unfamiliar with the theory of regulation may be tempted to inventclever ways for the regulator to provide full cost-minimizing incentives whileholding prices down to cost, but all will fail. The inevitability of this trade-off hasbeen established repeatedly and with great rigor; however, the trade-off can beimproved by improving the regulators effective knowledge.7 The main techniquefor making the trade-off is to adjust the price cap more or less frequently. Constantadjustment produces COS regulation while extremely infrequent adjustmentproduces pure price-cap regulation. In between, incentives are moderately strongand prices are moderately low. If the regulator has a fair amount of information,this trade-off can be quite satisfactory, but it will never equal perfect competition.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.12 PART 1 Power Market FundamentalsRegulation in PracticeCompetition can hold average prices down to long-run costs while putting fullstrength pressure on cost minimization. At best, regulation does a decent job ofboth but does neither quite as well as competition. But how does regulation workin practice?Regulation tends to err in the direction of driving prices down toward cost. Infact, most regulators believe this is their entire job and would implement pure COSregulation if they could. Fortunately, its just too much bother to re-adjust ratescontinuously, so the result is roughly a price cap that gets reset about every threeyears. This inadvertent regulatory lag is a major factor in saving COS regulationfromproviding no incentive at all. It provides some incentive for cost minimization,but less than would be provided with an optimal trade-off. Even that is too littleby the standard of a competitive market. In practice, regulation has typically donea passable job in the United States and could do much better if the effort spentderegulating were spent improving regulation.1-1.3 THE BENEFITS OF COMPETITIVE WHOLESALE MARKETSCompetition provides much stronger cost-minimizing incentives than typical cost-of-service regulation and results in suppliers making many kinds of cost-savinginnovations more quickly. These include labor saving techniques, more efficientrepairs, cheaper construction costs on new plants, and wiser investment choices.Distributed generation is an area in which innovation may be much quickerunder competition than under regulation; cogeneration is one example. Regulatedutilities found such projects extremely awkward at best, so avoided them. Acompetitive market easily allows the flexibility that such projects require.The other advantage of competition is its ability to hold price down to marginalcost. This is less of an advantage simply because traditional regulation has stressedthis side of the regulatory trade-off. Sometimes price minimization can still be asignificant advantage. Again cogeneration provides an example. Once regulatorsdecided to encourage it, they needed to price cogenerated power. A formula wasdesigned with the intention of mimicking a market price. Naturally, political forcesintervened and the result was long-term contracts signed at very high prices (Joskow2000b). These gave strong, probably much too strong, incentives for cogeneration.A competitive market can get both incentives and prices right at the same time.While holding down prices, competition also provides incentives for moreaccurate pricing. Because it imposes the real-time wholesale spot price on theretailers marginal purchases, wholesale competition should encourage real-timepricing for retail customers. This can be done easily by a regulated retailer, but acompetitive retailer should have an added incentive to provide the option of real-time retail pricing because that would reflect its costs.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-1 Why Deregulate? 138. For a comparison of demand-charges and real-time rates and an explanation of why real-time rates arecrucial for reducing market power, see Borenstein (2001b).1-1.4 THE BENEFITS OF REAL-TIME RATESOne view holds that the main benefit of competition will come from the demandside of the market more than the supply side. The price spikes of the wholesalemarket will be passed on to customersat least for marginal consumption and willcause customers to curb their demand when the price is highest and generation ismost costly. This will allow fewer generators to be built and will reduce the totalcost of providing power. A competitive market will pass this savings on to consum-ers.Arthur Wright of Brighton, England, invented the real-time meter which SamuelInsull heard of while visiting his homeland in 1894. He sent Louis Ferguson toBrighton to study its use. Insull soon replaced most of his meters with Wright real-time meters and by 1898 was installing them with every new residential hookup(Platt 1991). Although Ferguson invented the notion of charging according to thetime of peak demand, this was rarely used. Instead customers were charged for peakdemand (a demand charge) and total energy. This combination became knownas a Wright tariff. The purpose of such metering was to improve the systems loadfactor (average load over peak load), and it did so. Central station load curves fromChicago show that their load factor improved from 30.4% in 1898 to 41.7% elevenyears later. The Wright tariff is not real-time pricing but has a similar, thoughgenerally weaker, effect on peak demand.8The cost-saving effect of real-time pricing cannot be doubted, but how greatis it? Unfortunately it is much smaller today than it was in 1898, and that mayexplain in part why residential customers no longer have real-time meters. Todaysload factors are typically near 60%, although, in a system like Albertas whereregulators have imposed heavy demand charges, the load factor can approach80%. Real-time pricing could do the same. It can never cause load to becomecompletely constant (100% load factor) because this would put an end to real-timeprice fluctuations, and there would no longer be a reason for customers to shifttheir consumption off peak. Thus load-shifting caused by real-time pricing is self-limiting. Assume that the shift would proceed halfway if real-time pricing werefully implemented. Changing the load factor from 60% to 80% gives about a 25%reduction in needed generation capacity. This is dramatic, and perhaps a bit optimis-tic, so for numeric convenience, assume the reduction is only 24%.With an 80% load factor, most load would be baseload because high real-timeprices reduce peak load. Peaking generators cost roughly half of what an averagegenerator costs per installed megawatt. The reduction in generation fixed costsshould be in the neighborhood of 12%. Because fuel costs are about as large asthe fixed costs of generation, total wholesale power costs will be reduced only about6%. (Real-time pricing shifts load to off-peak hours but its effect on total energyconsumption is minimal and could work in either direction.) Wholesale costs areabout 3'8 the cost of retail power, so retail costs are reduced by about 2.25%.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.14 PART 1 Power Market Fundamentals9. Significant savings in transmission and distribution should not be expected because transmission linesare typically used most heavily during off-peak hours, and both have very large fixed-cost components thatwill be unaffected by deregulation.10. More kinetic energy is stored in rotating generators, much more potential energy can be stored bypumping water up hill and vastly more energy is stored in local fuel supplies, but all of these stores ofenergy must be converted to electrical energy by the process of generation before they can be delivered.Peak transmission use often occurs during shoulder hours, not peak hours, sothere is no easy proof of a transmission cost savings. But for simplicity assumethat this savings is 1'3 as great as the saving in generation. That brings total savingsto 3%.

Result 1-1.1 Savings from Real-Time Rates Would Be SmallFully implemented real-time pricing would improve load factors roughly from60% to 80%. This would reduce the cost of supply by approximately 2.25% ofretail costs mainly due to savings in peak-load capacity. Additional consumercosts of accomplishing the load shift would likely more than cancel any transmis-sion savings for a net savings of about 2% of retail costs. This 3% reduction in supply cost is offset by a cost increase on the demandside. Shifting load to off-peak hours is costly for customers as it requires thepurchase of smarter appliances and changes in consumption that they find undesir-able. In fact customers will shift load up to the point where the marginal cost ofshifting is just as great as the marginal savings on their electricity bill. A roughestimate puts the total cost to consumers at about 1'3 of the savings and this doesnot include the cost of the real-time metering and billing. The net savings from real-time metering should be in the neighborhood of 2% of total cost of deliveredpower.9A second question about real-time pricing as an argument for deregulation iswhy it cannot be done under regulation. Regulated systems have for years computedreal-time system marginal cost. Technically, it would be no problem for a regulatedutility to install real-time meters and charge customers marginal-cost prices.California is now testing this possibility (Wolak 2001). It may be that regulatorssimply lack the will to do this or the ability to carry out the details effectively. Onthe other hand, it may take more will and cleverness to implement a competitivewholesale market than to implement real-time pricing.1-1.5 PROBLEMS WITH DEREGULATING ELECTRICITYElectricity is a peculiar product. It is the only product that is consumed continuouslyby essentially all customers. In fact it is consumed within a tenth of a second ofits production and less than a tenth of a second of power can be stored as electricalenergy in the system.10 These physical properties result in a product whose marginalcost of production fluctuates rapidly and, thus, whose delivered cost also fluctuatesrapidly. No other product has a delivered cost that fluctuates nearly this rapidly.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-1 Why Deregulate? 1511. See J affe and Felder (1996), Kahn et al. (2001), and Green (1998).Two Demand-Side FlawsAlthough real-time metering began in the late 1800s, it has been discontinued forresidential customers, and almost no industrial or commercial customers see real-time prices. Consequently, almost no customers respond to the real-time fluctuationsin the delivered cost of power.Even with this demand-side flaw, the market could operate in reasonably closeaccord with economic principles if not for the second demand-side flaw, the abilityof a load to take power from the grid without a prior contract with a generator(Ruff 1999, 28; FERC 2001b, 4). If bilateral contracts could be enforced byphysically cutting off customers who exceed their contracts, the market couldfunction almost in alignment with the theory of competitive markets. In no othermarket is it impossible to physically enforce bilateral contracts on the time scaleof price fluctuations.

Demand-Side Flaw 1: Lack of Metering and Real-Time BillingDemand-Side Flaw 2: Lack of Real-Time Control of Power Flow to Specific CustomersThe first demand-side flaw causes a lack of demand responsiveness to priceor, technically, a lack of demand elasticity. The second demand-side flaw preventsphysical enforcement of bilateral contracts and results in the system operator beingthe default supplier in real time.Because demand responds only minimally to price, the supply and demand curvemay fail to intersect, a market flaw so severe it is not contemplated by any text oneconomics.11 The system operator, as default supplier, is forced to set the price,at least when supply fails to intersect demand. It can also improve the market bysetting price under slightly less dire circumstances. Presently, all power marketsoperate like this and will continue to do so until very-short-run demand elasticityis significantly improved.These are not just theoretical problems. While the average cost of productionis about $35/MWh, and the maximumcost with new equipment is about $100/MWh,prices in the $1,000 to $10,000 range have occurred in many markets. All four ofthe U.S. markets have formal price caps, and the Midwest market has informal capsset by system operators who refuse to buy required reserves when the price getstoo high. With the extreme demand inelasticity caused by the first flaw, scarcityalone would produce high prices, but the flawed demand side coupled with scarcityalso produces ideal conditions for market power which pushes prices still higher(J oskow 2001a).Dramatic though these flaws are, it should still be possible to design a well-functioning market. But it does require design! Deregulating power markets is calledrestructuring in the United States because the resulting competitive markets havemore federal regulations than the regulated markets they replaced (Borenstein andBushnell 2000). In the long run, the demand side of the market should developenough price elasticity to clear the market at a finite price. There is a good chanceFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.16 PART 1 Power Market Fundamentalsthat eventually price spikes will be low enough to need no caps. This change inmarket structure should be encouraged from the start. A responsible deregulationof electricity would first fix the demand-side flaws and then start the markettheyare cheaper to fix than the problems they have already caused.Complexity and Local Market PowerThere are two other fundamental problems with deregulating electricity: complexityand local market power. A power system is a delicate, single machine that canextend over millions of square miles. Every generator in the system must besynchronized to within a hundredth of a second with every other generator in theAC interconnection. Voltage must be maintained within a 5% limit at thousandsof separate locations. This must be accomplished on a shared facility, half of which(the grid) must be operated for the common good and half of which (the generators)are operated for hundreds of different private interests. Complexity can be overcome by a sufficiently well designed set of market rules,but the problem of local market power may need to be solved, at least for thepresent, by interventionist means. So far, it has been. More than half of the genera-tors in the California ISO were declared must run, meaning sometime duringthe year they were crucial to system operation and, therefore, had such extrememarket power there was no choice but to regulate their price. San Francisco andNew York among other cities are load pockets; they require more power thanthey can import. As a consequence, the two generators in San Francisco wouldhave extreme market power during peak hours every day if they were not regulated.These generators are required for their real power production, but most must-rungenerators are required for their reactive power, a concept not well understoodby regulators (see Chapter 5-2).The most difficult and costly problems with new electricity markets are mainlymatters of market structure as opposed to market architecture (see Chapters 1-7and 1-8). When this is understood, and demand-side flaws and the problems withmarket power and transmission are squarely faced, adequate solutions will probablybe found. Then wholesale power markets should prove superior to regulatedmonopoly generation.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Nothing is moreterriblethan activity without insight.Thomas Carlyle(1795-1881)Chapter 1-2What to DeregulateDELIVERED POWER IS A BUNDLE OF MANY SERVICES. These includetransmission, distribution, frequency control, and voltage support, as well asgeneration. The first two deliver the power while the second two maintain powerquality; other services provide reliability.Each service requires a separate market, and some require several markets. Thisraises many questions about which services should be deregulated and which shouldnot. Even within a market for a single service, one sideeither demand orsupplymay need to be regulated while the other side of the market can be deregu-lated. For instance, the supply of transmission rights must be determined by thesystem operator, but the demand side of this market is competitive. In contrast,the demands for ancillary services are determined by the system operator whilethe supply sides of these markets can be competitive. The most critical service in a regulated or a deregulated power market is thatprovided by the system operator. This is a coordination service. For a deregulatedmarket it typically includes operation of the real-time markets and a day-aheadmarket. These provide scheduling and balancing services, but operating thesemarkets is itself an entirely separate service. While the need for the systemoperatorservice is agreed to by all, the proper extent of that service is the subject of thecentral controversy in power market design.Chapter Summary 1-2: Many services are required to bring high-quality reliablepower to end users. Each might be provided by free markets, by the state, byregulated suppliers, or by some hybrid arrangement. Bulk power generation is thesource of nearly half the cost of retail power and is one of the services most easilyprovided by a competitive market. Moreover, it seems to offer several possibilitiesFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.18 PART 1 Power Market Fundamentalsfor significant efficiency improvements. If restructuring gets this much right, it willreap most of the benefits presently available from deregulation of electricity. Markets for reserves may be the next most sensible targets for deregulationbecause they are so closely tied to the bulk power market. Reserves are providedby the same generators that provide power. These markets can only be deregulatedon the supply side, and they are quite complicated to design. Retail deregulationis easier to design, and retailing can be more fully deregulated, but there is muchless to gain. Retail costs are at most 5% of total costs, and the potential savingsare less obvious than in generation because most of the traditional retail servicesare irrelevant. This is also the one area in which competition can be expected toadd a significant costthe cost of marketing.Section 1: Ancillary Services and the System Operator. The systemoperator must keep the system in balance by keeping supply equal to demand. Asmany as five markets may be required to accomplish this: one for regulationwhich works minute by minute, and four to handle larger deviations and emergen-cies. Collectively, these services, together with a few others, are known as ancillaryservices.Ancillary services benefit the entire market and are either public goods or havelarge external effects. Consequently, all of the markets have a fully regulateddemand side, but some can be deregulated on the supply side. The system operatorservice, which coordinates these markets and provides the regulated demand forancillary services, is a natural monopoly service and can be provided by a nonprofitor a for-profit entity.Section 2: Unit Commitment and Congestion Management. Traditionally(before restructuring), system operators provided two more coordination services:unit commitment and transmission-congestion management. Unit commitment canbe left to the generators themselves, though this may result in a small decrease inefficiency. Transmission congestion must be managed, at least in part, by the systemoperator.Section 3: Risk Management and Forward Markets. Both generators andtheir customers are risk averse and wish to avoid the fluctuating prices of the spotmarket. Not only the hour-to-hour and day-to-day price variations but also the year-to-year variations in the spot markets average price are problematic. Forwardenergy trading can hedge these risks and needs no more regulation than othercommodity markets.Section 4: Transmission and Distribution. Delivery of electric powerrequires a network of high voltage lines. Because duplicate sets of lines are wasteful,both distribution and transmission appear to be natural monopolies. There has beenFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-2 What to Deregulate 191. Markets for transmission rights that cover the cost of congestion already exist but not competitivemarkets for transmission lines. Australia and Argentina are experimenting with for-profit transmissionlines. A market for monopoly transco franchises is another possibility (Wilson 1997).2. Frequency is very precisely maintained as indicated by the following report (NERC 2000, 32). In lateJ uly 1999 . . . systemfrequency on the Eastern Interconnection dipped to one of its lowest levels in history(59.93 Hertz).speculation about granting rights to congestion rents to investors in transmissionlines and thereby stimulating a competitive market for such lines, but currently nojurisdiction plans to rely on such a market.1Section 5: Retail Competition. Retail service in electricity does not includedistribution of power to the customer. In its present form, it usually does not includemetering or even meter reading. Most retailing consists of financial transactions,all of which can be provided from an office building. There are relatively fewpossibilities for value added. Early on, deregulation advocates claimed that retailerswould provide innovative products (new types of meters and new qualities ofelectricity), but now their claims of innovation focus on billing.The use of green power and time-of-use billing seem to be the most substantiveimprovements available in the retail market, but there is little reason to believe thesecould not be provided by a regulated market. In fact, green power might be moreeasily provided under regulation. Unfortunately, because customers will want orrequire the right to switch suppliers, retail competition may make it more difficultfor generators to sign long-term contracts. This could make the wholesale marketmore risky and more susceptible to the exercise of market power.1-2.1 ANCILLARY SERVICES AND THE SYSTEM OPERATORThe system operator must keep the system in balance, keep the voltage at the rightlevel, and restart the system when it suffers a complete collapse. The systemoperator carries out these basic functions by purchasing what are called ancillaryservices. These include various types of reserves, voltage support, and black-startservices. Ancillary services are the subject of Chapter 3-2 where they are definedmore carefully and more broadly.Regulation and BalancingAny imbalance between supply and demand causes the systemfrequency to deviatefrom the standard (60 Hz in the United States).2 This is problematic for someappliances; nondigital clocks and phonographs depend on the system frequency,but large generators depend most on a constant frequency. Changing frequencymakes these enormous machines speed up or slow down, causing added wear andtear. Consequently, maintaining a precise system frequency is given high priorityFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.20 PART 1 Power Market Fundamentals3. See Chao and Wilson (1999a) and Wilson (1999).by the system operator. There seems to have been no cost-benefit analysis, butbalancing the system with some accuracy is absolutely necessary.System frequency is exactly the same for all customers in an interconnection.For example, Quebec and Florida have exactly the same frequency. As long as anysystemoperator maintains its frequency, every other system in the Eastern Intercon-nection will also have exactly the right frequency. As a result, no one has muchinterest in trying to maintain frequency. Economics calls this a free-rider problem.It is costly to maintain the system balance, and everyone would prefer to let theothers take care of it. Consequently, some regulatory body must decide to purchasebalancing services and must charge (tax) some market participants to pay for them.There is no alternative; with a pure free market approach, the system frequencywould be unacceptably unstable. This means the demand for balancing servicesmust be regulated, but they still can be supplied by a competitive market. Everysystem operator must meet a balancing standard set by the North American ElectricReliability Council (NERC), so it purchases enough balancing services to meetthis standard. Because many different generators can supply the services, there isa good chance the market will be competitive. But it is not automatic; it dependson the details of the market.Self-Provision of Reserves. There are two approaches to the supply of balancingservices. The system operator can purchase the necessary services in a market andassign the cost to either loads or generators on a pro rata basis, or it can assign eachsupplier a fraction of the physical requirement. The latter approach is called self-providing and is often described as a less regulated approach.3 As an example,consider spinning reserves (spin), a key source of balancing services. Not everygenerator will want to provide spin, so if physical requirements are imposed onsuppliers, a market for spin will develop. Those who find it expensive to providewill buy from those who can provide it more cheaply, and some generators willself-provide.What is the practical difference between the physical self-provision approachand the financial approach? Imagine that a supplier has been told to supply 100MWh of spin as part of its contribution to balancing services, and that it self-supplies. If the system operator had instead purchased spin directly and hadcharged the supplier for 100 MWh of spin, would the supplier have been worseoff? No. It would have sold its 100 MWh of spin to the market at the spin-marketprice, P, for a revenue of , and then the systemoperator would have charged 100Pit 100P for its share of the spin requirement. The result is the same. In both casesthe generator provides 100 MWh of spin. In neither case does it have any net cost.So why the agitation to self-provide? There are several possible answers. First,some may not understand the concept. Others may believe they can more easilysupply poor quality spin when they self-provide. Still others may not be interestedin their own requirement but may wish to provide part of the system-operatorservice. In other words, they may want to be the market maker for spin and takethis business away from the system operator. If they can do it more efficiently andFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-2 What to Deregulate 21with less gaming than the system operator, then they should be allowed to take overthis service.The problem with self-providing is that the services are not provided to thesuppliers themselves but to the system operator. The term is deceptive. There stillmust be a physical transaction between the supplier and the system operator. It isthis physical transaction, the verification of the provided reserves, that is difficult.Self-provision is not a way to avoid the regulated nature of the demand side ofthe ancillary service market, and it does not make the supply side more competitive.Voltage Support and Black-Start CapabilityMost generators need to take electric power from the grid in order to start them-selves. Consequently, if the system goes down, they cannot help it restart. Specialgenerators have the ability to self-start. Like balancing services, black-start servicesare a public good and must be purchased by the system operator.Voltage sags when too much reactive power is taken out of the system.Reactive power, unlike the real power that lights up incandescent lights, doesnot travel very well over power lines. When too much is used locally, for exampleby motors, fluorescent ballasts, and transmission lines, the voltage sags locally.To counteract this, more reactive power must be injected locally by capacitors,normal generators, or special generators called synchronous condensers.Reactive power is less of a public good than the other ancillary services. It ispossible, though expensive, to measure its use by individual customers and by thegrid. In principle, these could be charged for their use and there could be a spotmarket in reactive power. This would be a complex and expensive market to runalthough reactive power is usually very cheap to produce. Also, because of thedifficulty with transmitting reactive power over long distance, there would be farless competition in the reactive power market.Voltage support, like other ancillary services, has a free-rider problem unlessall customers are metered for its consumption. Customers lack sufficient incentiveto replace the reactive power they use because the voltage drop caused by onecustomer affects many others. Consequently, at a minimum, there is a need for aregulatory requirement for reactive power purchases. For the present, by far thesimplest approach is for the system operator to buy what is needed and, whennecessary because of market power, to regulate the purchase price.The System Operator ServiceThe system operator service, which coordinates the ancillary service markets andprovides the regulated demand for ancillary services, is a monopoly service (Ruff1999). This monopoly can be either a nonprofit or a for-profit entity. If nonprofitit is typically called an independent system operator (ISO) in the United Statesand can be minimally regulated. Transco is the current U.S. term for a for-profitsystem operator, an entity that will probably own the grid and will require extensiveregulation.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.22 PART 1 Power Market FundamentalsNonprofit monopolies are quite different from for-profit monopolies. Forinstance, an ISO will have no motive to maximize the rent from congested transmis-sion lines because it cannot keep that rent as profit. An unregulated for-profit systemoperator could have an extremely strong motive to maximize rent by withholdingtransmission service. Because such behavior is both unfair and inefficient, the for-profit system operator will need to be regulated. One opinion holds that the transmission grid will face competition fromdistrib-uted generation (small local generators) and is, therefore, no longer a naturalmonopoly. This was the case in 1890, but now such competition is extremely weak.Imagine a modern city being deprived of its importing transmission lines, and askif this would raise its cost of power if it were forced to rely on within-city distributedgeneration. It would be enormously expensive. The trend toward increased relianceon transmission has been apparent for more than a century, and deregulation hasonly accelerated this trend. New micro-generator technology has increased thechances for distributed generation to slow or reverse this trend, but the transmissionsystem will not lose its natural monopoly character for decades to come. Until then,transcos must be regulated.Although ISOs have no motive to extract monopoly rents, they do have aweakened motive to act efficiently. Their motivation comes mostly from publicscrutiny which is enhanced by the attention of market participants (stakeholders)who have a lot to lose from inefficient ISO operation.For the present, the system operator service must be provided by a regulatedfor-profit monopoly transco or by an lightly regulated nonprofit ISO. Both are poorchoices and may prove to have fairly similar problems. The Transmission Adminis-trator in Alberta, Canada, a for-profit regulated monopoly, is regulated in such away that it behaves like a nonprofit in many respects. For example, it proposedsubstituting large incentive payments and charges on generators for the buildingof a large new transmission line. While the line may not have been justified (thoughnow it claims it is), the incentives were structured in such a way that they appearedto make money for customers. The costs of inducing generation investment in morecostly locations were both hidden and denied. The monopoly transcos incentiveto optimize transmission was extremely weak to nonexistent. Instead, it exhibitedthe same interest as an ISO in gaining favor with the public and stakeholders.There is one possible way out of this dilemma. Monopolies may sometimesbe forced to compete by granting them a temporary franchise which can be wonthrough a bidding process. Robert Wilson (1997) has proposed doing this and hassuggested a scheme for providing them with incentives for efficient system opera-tion. Although this approach shows promise, the technical and political problemswith implementation are still formidable.1-2.2 UNIT COMMITMENT AND CONGESTION MANAGEMENTThere is nearly universal agreement that the system operator must run the real-timemarket, and that the demand for ancillary services must be determined by a centralauthority. But the services of unit commitment and congestion management havecaused a great controversy. This is often referred to as the Poolco or nodalFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-2 What to Deregulate 234. More recently Hogan (2001b) has explicitly suggested designs that make the unit commitment serviceoptional.5. No-load costs, which are greater than startup costs, also cause the production cost function to benonconvex, but they apparently cause less trouble.pricing debate. Professor William Hogan of Harvard has put forward the nodal-pricing model which has now been accepted by PJ M and the New York, and NewEngland ISOs. California, Australia, Alberta, and England have rejected it in favorof a less centralized approach.Hogan (1992, 1995, 1998) specifies a system operator that provides both unitcommitment and congestion management services.4 These two are linked togethermore because of historical system operator practice or by choice than by logic. Infact, the system operator could easily provide only congestion management andbalancing, but not unit commitment.The Unit Commitment ServiceThe unit commitment service need not be centrally provided nor even be providedby a private market. Each generator can provide it for itself. This service simplytells generators when to turn on, how much to produce at each point in time, andwhen to turn off. These decisions can be made privately. The question is, howefficiently will they be made.If decisions are private, individual generators will predict the price of energyduring the time under consideration and will then incur the cost of starting up ifthey expect to make a profit. When shutting down appears to be more profitablethan running, they will shut down. Economic analysis shows this process worksalmost perfectly if price predictions are perfect and there are no costs to startingand stopping. In real markets, however, neither assumption applies. This raisestwo questions: (1) would the system operator predict prices more accurately, and(2) can the system operator work around the problem of startup costs more effi-ciently?The system operator can probably predict market price slightly better thanindividual suppliers because it has more information, but this advantage may notbe great. Under nodal pricing, the system operator can predict the day-ahead pricewhen it schedules, but it is the unknown real-time price that matters.The inefficiency described by economic theory and caused by nonconvexstartup-costs is almost certainly very small.5 (This is discussed at length in Chapter3-8.) Although startup costs probably do little damage to the market equilibrium,they make it more difficult to find. This might be a greater source of inefficiency,particularly if this problem interacts with reliability. Currently, there is little, if any,evidence that the system operator can save much by performing the unit commit-ment service. But there is little to lose and perhaps a noticeable gain, especiallyin a new market, so the safe course may be to have the system operator providethe service and make it optional. This is now done by PJM and almost all producersmake use of the service. But the implications are unclear because of indirectincentives to accept PJ Ms service.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.24 PART 1 Power Market Fundamentals6. If the systemoperator sells transmission rights and collects the congestion rent, it can sell the rights ona daily or hourly basis in the formof nodal pricing, or it can sell yearly or monthly transmission rights inperiodic auctions, or these can be combined or supplemented with other approaches.Transmission-Congestion ManagementCongestion management is one of the toughest problems in electricity marketdesign. Although the costs imposed by congestion in an efficiently run system arequite low, badly designed congestion pricing can make the system unmanageable.This was demonstrated by PJ M just before the official opening of its market whenit instituted a form of average-cost congestion pricing that resulted in massivegaming of the pricing rules (Hogan 1999).Any efficient method of congestion management will charge for the use ofcongested lines. If the price charged is set correctly, the demand for the use of theline will equal its capacity unless the price is zero, and it will be zero only if at zeroprice the line is still not fully utilized. Pricing ensures that those who value the linemost get to use it and that the lines capacity is not wasted. This is the only efficientway to manage congestion.Although there is only one set of efficient congestion prices (the prices set bythe nodal pricing approach), there are many other approaches that would in theorygive these same prices, or a good approximation of them. Wu and Varaiya proposedthe most extreme alternative to nodal pricing. In their multi-lateral approach (Wuand Varaiya 1995; Varaiya 1996), the system operator would have no knowledgeof the congestion prices. It would simply assign certain parties the right to use linesin a reasonable but arbitrary way that would prevent overuse of the lines. Theseparties would then either exercise their rights by using the lines or would sell theirrights to those who valued the lines more. If it worked efficiently as a competitivemarket should, the market would then produce the exact same prices for the useof congested lines as the system operator would compute under nodal pricing.Congestion prices make money by charging transmission users for a scarceresource. The revenues collected are called the congestion rent. Because congestionprices are the same under any efficient system, so is the congestion rent. Undernodal pricing, the systemoperator collects the congestion rent. Under other systems,such as the multi-lateral approach, some private party will collect these rents. Thisis at the heart of a controversy. When generators ask to self-manage their conges-tion, they are really asking to self-collect as much of the transmission rent aspossible.Any system of allocating transmission rights can be thought of as selling orgiving away transmission rights. In either case the rights originate with the systemoperator and are specified in such a way that the transmission lines are protectedfrom overuse. The supply of transmission rights must always be regulated.There is a fundamental choice to be made: should the system operator sell thetransmission rights and use the revenues (congestion rents) to help pay for the costof the wires, or should the system operator give the rights away and let privateparties pocket the congestion rents?6 Where physical rights have been purchasedin the past or been acquired by paying for lines or upgrades, grandfathering theserights, and perhaps converting themto financial rights provides regulatory continuityFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-2 What to Deregulate 25and enhances regulatory credibility. Other schemes for giving away new rights areusually obscure and arbitrary. Except when there is clear ownership of rights tobegin with, it is preferable for the system operator to create transmission rights,sell them, and use the resulting revenues to pay for present or future transmissionlines.1-2.3 RISK MANAGEMENT AND FORWARD MARKETSThe system operator needs to manage the system in real time to keep it physicallysecure. It also needs a small lead time for planning (scheduling). This lead timeis generally accepted to be approximately a day, but beyond that, the systemoperator has no need to pay attention to the energy market (transmission andgeneration capacity is another matter).Both generators and their customers will want to make long-term arrangementsfor the supply of power either in decentralized forward markets or in highly central-ized futures markets. The futures markets will work best if subject to the normalregulations imposed on commodities markets, but electricity futures need no specialtreatment. These markets should be just as deregulated as any other commoditymarket.Transmission rights also need forward markets. (See Hogan, 1997, for onemarket design.) As with congestion management, the system operator may playa role in the supply of transmission forwards because ultimately it must decide howmuch power will be allowed to flow on the various transmission lines. Unfortu-nately, transmission rights are extremely complex because, in present transmissionsystems, it is impossible to choose the path over which power will flow. If thereis a line from A to B and a trader owns only the right to transmit 100 MW over thatline, the trader will not have sufficient rights to make any trade at all. If even 10MW is injected at A and removed at B, a significant fraction of that power, some-times more than half, will flow on other lines. Where the power actually flows isdetermined by the laws of physics.Fortunately, designing forward transmission rights as purely financial rightscan simplify the problem of physical flows. A transmission right for 100 MW canconfer on its owner the right to the congestion rent from A to B times 100 MW.If the congestion rent averaged $10/MWh during peak hours, and the right covers100 MW of flow for 320 peak hours, the owner receives $320,000. With such rightsthe owners can perfectly hedge a transaction from A to B. The markets for suchrights need no special regulation, but they may not be liquid enough to serve theneeds of power traders fully. Much work remains to be done in designing betterhedges for congestion costs.1-2.4 TRANSMISSION AND DISTRIBUTIONIf the congestion rent is paid to the owners of transmission lines, too few lines willbe built. The market for transmission lines cannot be left unregulated, and evena regulated market may not be up to the job. One way to get lines built is to haveFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.26 PART 1 Power Market Fundamentals7. According to J oskow (2000a, 29), the total cost of retailing services amounts to between 3.3% and4.7% of total retail revenue. A reduction by half would at most amount to a savings of 2.4%.an ISO build them. Another way is to grant one company, a transco, the monopolyright to all lines in some large geographical area. Like any monopoly of an essentialproduct, the transco will need regulation.Several problems need to be considered. Transmission lines can act as botha substitute for and a complement to generation. New transmission lines increasecompetition between suppliers who may therefore oppose them, but they are apublic good because they reduce market power. The siting of a new transmissionline is a highly regulated and contentious process. It is also difficult to assignindividual physical or financial rights to the power grid in such a way that investorsmake the appropriate return on their investment.These complexities make deregulation of the market for transmission linesimpossible. The distribution system seems even more difficult to deregulate, andso far there have been few, if any, proposals to do so.1-2.5 RETAIL COMPETITIONThe push to deregulate generation was clearly predicated on reducing the cost ofgeneration which accounts for nearly one half the cost of power. Wholesale compe-tition could save a lot of money; retail competition needs a different rationale. Whenthe costs of the electricity industry are analyzed, they are traditionally divided intothree major categories: generation, transmission, and distributionretail is notmentioned. Retail costs could be cut in half, and no one would notice as they areonly a small fraction of distribution costs.7What is retailing? It is not distributing power at the local level or even hookingup individual customers. It is typically only financial transactions and sending outbills; occasionally it involves meter reading. Generally, a retailer buys wholesalepower, signs up retail customers, and sends out bills. Although an individual retailermay manage to purchase power cheaply, on average a retailer will pay the averagecost of wholesale power. Also, there is no reason to believe that competition onthe demand side of this market will reduce the cost on the supply side. There maybe room to cut billing costs, but there are other motives at work in the push for retailcompetition.The impetus for retail competition comes primarily from two sources: thosewho believe they can profit by being retailers, and big commercial and industrialcustomers. Some of them believe they are smarter or more desirable customersand so can cut a better deal on their own. These motivations, though strong, donot translate into politically persuasive arguments, so more theoretical explanationsare proffered. These fall into three categories: customer choice, innovative products,and price competition.Customer ChoiceAlthough those pushing hardest for retail competition are not particularly green,their main example of customer choice is that of green power. This could have beenFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-2 What to Deregulate 278. Though competition has spurred innovation in telecom, if competition had arrived forty years earlier,we would not have had vacuum-tube cell phones in the 1950s. Much of what is taken to be the miracle oftelecomcompetition is just normal technological progress.9. See Littlechild (2000, 11).provided quite easily under regulation, but it wasnt, so the green choice may bea benefit of retail competition. It allows customers to pay a premium for their energyand then makes sure some of that premium finds its way to generators that userenewable energy sources. One disadvantage of retail competition is that it makes verifying the reality ofthis product much more difficult. Physically, green power is identical in all respectsto coal power. The consumer cannot verify the product without the help of somethird party to audit the suppliers. The source of power is more difficult to monitorwhen there are many competitive green and semi-green private companies insteadof just one regulated utility.Another choice, often suggested but so far not implemented, is the choice ofreliability level. Clearly, some customers have a much greater need for reliability,and this is the one way in which electricity service can differ between customers.It is not possible to provide a more stable frequency or better voltage support ona customer by customer basis, but some reliability (avoidance of some blackouts)can be provided individually. This would require installing remotely controlledindividual circuit breakers. Unfortunately this is currently quite impractical. Partof the problem is that those with a strong financial interest in this service are thosewho want more reliability. This cannot be provided by installing a breaker for them;it must be provided by installing breakers for a great many others who would besacrificed in an emergency to provide reliability for those who would pay for it.Innovative ProductsOne view holds that competition in retail electricity will spawn innovative newelectrical products the way competition in telecommunications has spawned newtypes of phones and phone services.8 But so far AC power has shown no prospectsof becoming wireless. Power engineering went through a period of rapid innovationbetween 1870 and 1910 that was similar to the current innovation in telecommunica-tions, and someday it may again. Technology has a life of its own. Competitionmay spur some development of new generating technologies, but the basic AC outletwill be around for a while.Those who promised dramatic new physical innovations in retail power fiveyears ago have now shifted their focus from new kinds of electricity meters andsmart appliances to innovative billing systems. Would they have held telecommuni-cations up as an example of the benefits of deregulation if the last fifteen years hadproduced only more complex phone bills while telephones remained rotary dial?The argument for the value of billing innovations is a curious one. In England,electricity deregulation has brought some of the same aggravation to electricityshopping that U.S. customers experience in shopping for phone service. Littlechildargues that the fact that customers spend so much effort comparing rates provesthey must benefit from doing so.9 Perhaps customers draw a different conclusionFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.28 PART 1 Power Market Fundamentals10. Recently, and long after this section was written, this phenomenon was documented in the PJ M marketby Michael Rothkopf, who was the recipient of an offer to pay 38% above the going rate with only extracancellation penalties as compensation. In California deceptive practices similar to those found in phone-rate competition were quickly spotted in the retail power market.than economists because they understand their efforts are as much to avoid badrates that were previously not a danger as to find good rates that were previouslynot available.10 In any case, other than real-time pricing, it is hard to imagine howbetter electricity bills can bring much improvement to the life of the averagecustomer.Price CompetitionThe latest rationale for retail competition is the benefit of price competition. Evenif customers dont think fancy electric bills are as useful as cell phones, cheaperbills would certainly prove popular. Littlechild (2000, p. 9) pushes price competitionas the major benefit of retail competition and lists two ways this can happen, first,by reducing the costs of retailing. Unfortunately, as already noted, the costs ofretailing electricity under regulation are exceptionally small. Even with massiveimprovements in efficiency, customers will probably not notice a difference, andit is quite possible that marketing costs will more than offset any efficiency gains. Littlechild also mentions a reduction in wholesale costs caused by improvingwholesale power procurement. Where does this savings come from: better genera-tors, better operation, or a reduction in market power? With or without retailcompetition, generators still keep every dollar they save, no more and no less, soretail competition cannot possibly improve the cost-minimizing incentives ofgenerators. With costs the same, the only room for savings is a reduction in profit.Because the industry cannot survive on below normal profits, this can only comeabout if there is some excess profit at the outset.So retail competition can only lower wholesale costs by reducing the marketpower of wholesalers. But market power on the supply side of the wholesale marketwould normally be reduced by an increase in competition on the supply side, notby increased competition on the buyers (retailers) side. In fact more competitionon the buyers side means less monopsony power to counteract the monopoly powerof the suppliers.There appears to be only one small chance for retail competition to inhibitwholesale market power. If retailers sign long-term contracts with wholesalers,the contracts will inhibit the wholesalers market power in the spot market. Unfortu-nately, competitive retailers have a more, not less, difficult time signing long-termcontracts than the monopoly utility-distribution companies (UDCs) because theircustomer base is less stable. The customers of the UDC cant leave if there is noretail competition, but customers of competitive retailers generally can leave onfairly short notice and will leave if they do not like the current price. This makesit difficult for competitive retailers to sign long-term power contracts, especiallyfor the supply of residential customers. If the retailer buys its power with a long-term contract and sells it to customers under short-term contracts, it takes anenormous risk. If the market price goes down in the future, the retailer must eitherFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-2 What to Deregulate 29sell at a loss to its residential customers or lose them and resell its power at a lossto someone else.The net result seems to be that retail competition offers no benefits in reducingwholesale market power. As it will not bring down the costs of generation, it seemsto hold little promise of improving wholesale performance. The slim hope that pricecompetition will save more on billing costs than it spends on marketing is a flimsybasis for such a large experiment.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. In Tables 14 through 17 of one such report (DOE 1998a) the useful (amortized) fixed costs are notreported, and the fixed O&M costs are reported in $/kW which may be an amortized value reported withthe wrong units or, if the units are correct, may represent a misguided conversion of an amortized cost toan overnight cost.It is not too much to expect that our children will enjoy in their homeselectricity too cheap to meter.Lewis L. StraussChairman, Atomic Energy Commission1954Chapter 1-3Pricing Power, Energy, and CapacityPOWER IS THE RATE OF FLOW OF ENERGY. Similarly, generating capacity,the ability to produce power is itself a flow. A megawatt (MW) of capacity is worthlittle if it lasts only a minute just as a MW of power delivered for only a minuteis worth little. But a MW of power or capacity that flows for a year is quite valuable.The price of both power and energy can be measured in $/MWh, and sincecapacity is a flow like power and measured in MW, like power, it is priced likepower, in $/MWh. Many find this confusing, but an examination of screening curvesshows that this is traditional (as well as necessary). Since fixed costs are mainlythe cost of capacity they are measured in $/MWh and can be added to variable coststo find total cost in $/MWh.When generation cost data are presented, capacity cost is usually stated in $/kW.This is the cost of the flow of capacity produced by a generator over its lifetime,so the true (but unstated) units are $/kW-lifetime. This cost provides useful informa-tion but only for the purpose of finding fixed costs that can be expressed in $/MWh.No other useful economic computation can be performed with the overnight costof capacity given in $/kW because they cannot be compared with other costs untillevelized. While the U.S. Department of Energy sometimes computes theseeconomically useful (levelized) fixed costs, it never publishes them. Instead itcombines them with variable costs and reports total levelized energy costs.1 Thisis the result of a widespread lack of understanding of the nature of capacity costs.Confusion over units causes too many different units to be used, and this requiresunnecessary and sometimes impossible conversions. This chapter shows how tomake almost all relevant economic calculations by expressing almost all prices andFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-3 Pricing Power, Energy, and Capacity 31Working SummaryReaders wishing to gain only a working knowledgeof measurement units for use in later chaptersshould understand the following.Quantity Quantity units Price UnitsEnergy MWh $/MWhPower MW $/MWhCapacity MW $/MWhCost Symbol Cost UnitsFixed FC $/MWhVariable VC $/MWhAverage ACK=FC +cf VC $/MWhAverage ACE=FC'cf +VC $/MWhRatio Symbol UnitsCapacity factor cf noneDuration D noneNotes: Energy is a static amount while power andcapacity are rates of flow. The average cost of usingcapacity, ACK, depends on the capacity factor, cf ,which is the fraction of time the capacity is used. Theaverage cost of energy, ACE, produced by a specificgenerator also depends on cf .costs in dollars per megawatt-hour ($/MWh). The remainder of the book confirmsthis by working every example in these units.Chapter Summary 1-3: Energy is measured in MWh, while power and capacityare measured in MW. All three are priced in $/MWh, as are fixed and variable costs.Other units with the same dimensions (money divided by energy) may be used,but this book will use only $/MWh. Screening curves plot average cost as a functionof capacity factor. The slope of the curve is variable cost, and the intercept is fixedcost. The average cost (ACK) plotted in these graphs is not the average cost of usinga megawatt-hour of energy produced at a certain capacity factor but rather theaverage cost of a megawatt-hour of generating capacity. Because the equation fora screening curve is used through the book, understanding this distinction is crucial.Section 1: Measuring Power and Energy. Poweris the flow of energy and is measured in watts (W),kilowatts (kW), megawatts (MW), or gigawatts (GW).Energy is an accumulation of power over a period oftime. For instance, a kilowatt flowing for one hourdelivers a kilowatt-hour (kWh) of energy. The priceof both energy and power is expressed in $/MWh. Itcan also be expressed in mills, short for milli-dol-lars per kilowatt hour, with 1 mill equal to $1/MWh.Section 2: Measuring Capacity. Capacity is thepotential to deliver power and is measured in mega-watts. Like power, it is a flow.Section 3: Pricing Capacity. Overnight capacitycosts are measured in $/kW and so cannot be addedto or averaged with variable costs to find which gener-ator could more cheaply serve load of a specific dura-tion. Screening curves plot the annual revenue require-ment (ARR) of a generator as a function of the genera-tions capacity factor. Fixed cost (FC) is the value ofARR for a capacity factor of zero. Since ARR is mea-sured in $/kWy, the same must be true of fixed cost.Dividing FC by 8.76 converts it to $/MWh, a moreconvenient set of units. Considering the rental cost ofcapacity makes these units seem more natural. To avoid confusion when using screening curves and their associated algebra,the distinction between the average cost of capacity (ACK) and the average costof energy (ACE) should be kept in mind. Traditional screening curves graph ACK.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.32 PART 1 Power Market Fundamentals2. Watts per hour has units of watts divided by hours and has no use in the present context. 3. Average revenue per kilowatt hour to ultimateresidential consumers was 8.06/kWh, according to DOE(2001c, Table 53).Unit ArithmeticUnitskilowatts, hours, and dollarsfollow thenormal laws of arithmetic. But it must be understoodthat a kWh means a (kW h) and a $ per hourmeans a ($/h).Also note that 8760 hours per year has the valueof 1, because it equals (8760 h)'(1 year), and(8760 h) =(1 year).As an example, $100/kWy =$100 1000kW 1year

kWyear 1MW 8760hwhich reduces to $11.42/MWh.1-3.1 MEASURING POWER AND ENERGYPower Versus EnergyPower is the rate of flow of energy. This is true for any form of energy, not justelectricity. If you wish to boil a cup of water you need a quantity of energy to getthe job done, about 30 watt-hours. Any specific power level, say a thousand watts(kilowatt, or kW), may or may not make you a cup oftea depending on how long the power continues toflow. A typical microwave oven delivers power at arate of about 1 kW (not 1 kW per hour). If it heats yourwater for one second, the water will receive power atthe rate of one thousand watts, but it will gain verylittle energy and it will not make tea. Two minutes inthe micro-wave will deliver the necessary energy, 1'30of a kWh.Confusion arises because it is more common tohave the time unit in the measurement of a flow thanin the measurement of a quantity. Thus if you want tofill your gas tank, you buy a quantity of 15 gallons ofgasoline, and that flows into your tank at the rate of5 gallons per minute. But if you need a quantity ofelectric energy, that would be 30 watt-hours, and it would be delivered at the rateof 1000 watts.2 Because a watt-hour is a unit of energy, it would make sense tospeak of delivering 1000 watt-hours per hour, but that just boils down to a rate of1000 watts (1 kW) because a watt-hour per hour means watts times hours dividedby hours, and the hours cancel out.The Price of Power and EnergyBecause power is a flow, its total cost is measured in dollars per hour, not dollars.The total cost of a certain quantity of energy is measured in dollars. Consequentlythe price (per unit cost) of power is measured in dollars per hour per MW of powerflow, while the price of energy is measured in dollars per MWh. But these unitsare the same:(dollars per hour) per MW=($/h)/MW=$/MWhso the units for the price of power are the same as for the price of energy.Typically the price of retail energy is about 8/kWh.3 At that price, the priceof power would be 8 cents/hour for a kilowatt of power flow, which is the same.These units are convenient for home use but are inconveniently small for bulk powersystems. Consequently this book will use megawatts (millions of watts) insteadFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-3 Pricing Power, Energy, and Capacity 334. The flow of available capacity is interrupted during generator outages, but the flow of installed capacityis continuous. This chapter ignores the difference and assumes that the flow of capacity froma generatoris continuous and constant.of kilowatts. The same energy price can be re-expressed as $80/MWh. Whendiscussing large markets and annual energy use, power may be measured ingigawatts (GW, or billions of watts) and energy in terawatt hours (TWh, or trillionsof watt hours).Another commonly used unit is the mill, short for milli-dollar, or of a1'1000dollar. This unit might seem particularly inappropriate for wholesale markets, butit is commonly used to compensate for using the kW which is also inappropriatelysmall. Together these give rise to milli-dollars per kilowatt-hour, often incorrectlyshortened to mills. Scaling both the numerator and denominator up by 1000 hasno effect on the numeric value and converts milli-dollars to dollars and kilowattsto megawatts. So 80 mills/kWh is identical to $80/MWh.1-3.2 MEASURING GENERATION CAPACITYThe size of a generator is measured by the maximum flow of power it can produceand therefore is measured in MW. The capacity to produce a flow of power is bestconceptualized as a flow just as a MW of power is a flow of energy.4In principle one could define an amount of capacity related to the flow ofcapacity as energy is related to power, but this is not necessary. Moreover, it is likelyto cause confusion because when applied to a generator, it would aggregate a flowof capacity over many years without any discounting. For these reasons, the ideaof a capacity amount, different from a capacity flow, will not be introduced orutilized.Having found that capacity, like power, is a flow measured in MW, it is naturalto ask if it is priced in $/MWh as is power. Most would say no, but it is best to lookto its use in solving real economic problems before drawing this conclusion.Consider the problem of choosing which generator can most cheaply serve a loadof a particular duration. The long tradition of solving this problem by usingscreening curves will provide the key to this puzzle.1-3.3 PRICING GENERATION CAPACITYThe Overnight Cost of CapacityA generator has an overnight cost which is typically given in $/kW. For example,the overnight cost of a coal plant might be $1,050/kW, so a 1000 MW plant wouldcost $1,050 million. In economic terms, this is the present-value cost of the plant;it would have to be paid as a lump sum up front to pay completely for its construc-tion.A conventional gas-turbine generator (GT) would have an overnight cost closerto $350/kW. Although the GT is three times cheaper than the coal plant, for someFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.34 PART 1 Power Market Fundamentals5. Duration is measured as a percentage (see Chapter 1-4), so if all load served has the same duration, thecapacity factor equals load duration. If the load has a range of durations, these must be averaged.6. For simplicity, this assumes that fuel is the only variable cost. Operation and maintenance include anadditional variable cost component which should be expressed in $/kWy.purposes the coal plant is the more inexpensive choice. Fuel costs must alwaysbe taken into account when evaluating the choice of generators. Coal plants arebuilt because their cost of fuel per unit of energy output is less. Assume coal costsonly $10/MWh of energy produced, while the cost of fuel for a GT comes to$35/MWh. Now which plant is cheaper?More information is needed. The comparison depends on how much the plantwill be used, and that depends on the load it will serve. For concreteness, assumethat the load has a duration of 25% (2190 hours/year) so the plant serving it willhave a capacity factor of 25%. Now, which plant is cheaper?Focusing on only the basics, the problem seems workable. The overnight costcaptures the fixed cost of generation, and the fuel cost per unit of output capturesthe variable cost. Duration gives a sufficient description of the load. But theproblem is still impossible to solve because the fixed cost of capacity has beenmeasured in the wrong units. Overnight costs measured in $/kW cannot be addedto fuel costs measured in $/kWh. This would produce nonsense.

F FF Fallacy allacy allacy allacy 1-3.1 Fixed and Variable Costs Are Measured in Different UnitsBecause capacity is usually paid all at once, while fuel is paid for over time,variable costs but not fixed costs should include a time dimension. When units have the same dimensions, they differ only by a scale factor (apure number). Different quantities having units of the same dimension can be added.For example, 1 MWh can be added to 100 kWh to get 1100 kWh (or 1.1 MWh).But quantities whose units have different dimensions cannot be added. This is themeaning of the famous saying, you cant add apples and oranges. For example,1 MW cannot be added to 1 MWh. Engineers and physicists pay close attentionto mismatched units because they always signal deeper trouble. Any calculationthat involves adding MW and MWh simply does not make sense.Identifying Fixed Costs on Screening CurvesScreening curves, shown in Figure 1-3.1, are used to compare generation costs bytaking account of the three factors of our present problem: fixed cost, variable costsand load duration (which determines the generators capacity factor). Necessarily,they provide guidance on the proper units for fixed costs. Traditionally, these curvesplot annual revenue requirement per kW (ARR) as a function of capacity factor(cf ). The generators capacity factor is its percentage utilization which is deter-mined by the loads duration.5Traditionally, the variable cost component of ARR is computed by taking thefuel cost expressed in $/MWh and converting to $/kWy.6 The result is $87.60/kWyfor a coal plant and $306.60/kWy for a GT. This assumes full-time operation, soFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-3 Pricing Power, Energy, and Capacity 357. Using monthly instead of annual compounding in the second formula greatly improves its accuracy asan approximation. To do this, change r to r'12 in the denominator and T to 12T.Figure 1-3.1Use of screening curvesto select a generator.to find the variable component for any particular cf , these must be multiplied bycf , 25% in the case of the present example.The overnight cost of capacity is more problematic. A coal plant with anovernight cost of $1,000/kW does not cost $1,000/kWy. This would imply a plantlife-time of one year and a discount rate of zero. The correct fixed-cost componentof ARR is the overnight cost amortized (levelized) over the life of the plant. Thisis equivalent to computing home mortgage payments based on a mortgage that laststhe life of the house. Obviously a discount rate (interest rate) is involved. Theformula for amortization is(1-3.1) FCr OCer OCrrT T=

1 1 1 1 / ( )Notice that fixed cost (FC) depends only on overnight cost (OC), the discount rate(r, in % per year) and the life of the plant (T, in years).7

Table 1-3.1 Technology CostsTechnologyVC( /MWh)VC( /kWy)OC( /kW)FC( /kWy)FC( /MWh)Gas turbine $35 $87.60 $350 $109.96 $12.21Coal $10 $306.60 $1050 $40.48 $4.62Fixed-costs are based on r =0.1 and on T =20 for gas turbines and 40 for coal plants. Equation 1-3.1gives fixed costs in $/kWh which are then converted to $/MWh by dividing by 8.76. FC is a constant flow of cost that when added to VC gives ARR, the annualrevenue requirement per kW of generation capacity. Of course this assumes acapacity factor of 1. If cf is less, VC will be reduced proportionally, but FC isunaffected because capacity must be paid for whether used or not. That is why FCis termed the fixed cost. The formula for ARR isScreening Curve: ARR =FC + cf VCFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.36 PART 1 Power Market Fundamentalsfor ARR to be valued in $/kWy, both FC and cf VC must also be valued in $/kWy.As these are the traditional units for ARR, the traditional units for fixed cost mustalso be $/kWy. These units have the same dimension as $/MWh and any quantityexpressed in $/kWy can be converted to $/MWh by dividing by 8.76.Variable cost is naturally expressed in $/MWh, so capacity factor, cf , must bea pure number (dimensionless), otherwise, cf VC would not have the same unitsas ARR. This is correct; a capacity factor is just the fraction of a generators potentialoutput that is actually produced. It is actual energy output divided by potentialenergy output, so the energy units cancel.

Result 1-3.2 Energy, Power, and Capacity Are Priced in $/MWhAlthough power is measured in MW and energy in MWh, both are priced in$/MWh. Like power, generating capacity is a flow measured in MW and conse-quently is also priced in $/MWh. The Rental Cost of CapacityFixed costs are the costs of generation capacity. It may be argued that buying agenerator is buying capacity and that generators are measured in MW, not in MWh.This is only partially true. If a 1 MW gas-turbine generator is worth $350,000, doesthis mean 1 MW of capacity is worth $350,000? No, the gas turbine is worth thatonly because it has a certain expected lifetime. An identical but older gas turbineis worth less, even though it has the same 1 MW capacity. Thus the price of capacityalways involves a time dimension, either explicitly or implicitly.Measuring capacity in MW indicates that capacity is being considered a flow.A 100-MW generator delivers a 100-MW flow of capacity for some unspecifiedperiod of time. That flow must be paid for by a flow of moneyso many dollarsper hour. This corresponds to a rental cost. If a generator is rented, the cost ofrenting will be so much per hour, or per day, or per year. If this is scaled by thegenerators capacity, for easy comparison with the rental rate of other generators,then it is natural to express the rental cost of a generator in $/h per MW, or equiva-lently in $/MWh.The above screening curve analysis can be summarized as saying that generationcapacity costs should be expressed as a rental rate and not as a one-time (overnight)purchase price. Rental rates naturally have the same units as variable costs and somake total and average cost calculations convenient.Two Kinds of Average Cost: Avoiding ConfusionThe cost of operating a generator with a specific capacity factor can be read froma screening curve. Traditionally this cost is expressed in $/kWy and called an annualcost. Although a kWy has the dimensions of energy, this cost is not the annual costof energy produced by the plant! A screening curve shows the average cost of usingthe coal plants capacity.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-3 Pricing Power, Energy, and Capacity 37Figure 1-3.2Capacity-cost based andenergy-cost basedscreening curves.Screening CurvesA traditional screening curve plots average cost asa function of capacity factor. When using the screen-ing curve equation, this average cost can be con-fused with the average cost of the energy producedby a certain type of generator. Instead, it is theaverage cost of using a unit of capacity.Screening curves could have been defined usingthe average cost of energy. Then as the capacityfactor approached zero the average cost wouldapproach infinity. The average-energy-cost equationis used to analyze market equilibria in later chapters,but nonstandard screening curves are never used.With the price of energy always expressed as an hourly cost, it is more conve-nient to divide the annual cost, in $/kWy, by 8.76 and arrive at an average cost perhour for the year expressed in $/MWh. Like the annual cost, this hourly averagecost is still not a cost of energy produced but the cost of using capacity. This bookwill always report capacity, energy and power costs in $/MWh for ease of compari-son and to make addition of costs and cost averaging possible.Although screening curves plot the average cost of capacity use, the averagecost of energy produced is also interesting and could be used to construct hyperbolicscreening curves. A pair of these is shown on the right side of Figure 1-3.2; theyare nonlinear (hyperbolic), but they still intersect at exactly the capacity factor atwhich one plant becomes more economical than the other. The equations for thelinear and hyperbolic screening curves are closely related and are shown in Figure1-3.2.The average cost of capacity (ACK) used with capacity factor cf is the fixed costof using that capacity, plus cf times the variable cost of producing energy. If, then one third of the variable cost of maximum potential energy output cf =1'3must be added to the constant fixed cost which increases the average cost per unitof capacity by cf VC.The average cost of energy (ACE) when the genera-tor runs with capacity factor cf is the variable cost ofproducing that energy, plus the fixed cost of the capac-ity divided by cf . If cf =1'3, then fixed costs must bespread over only 1'3 of the total possible energy output,so they are multiplied by 3 (divided by cf ) before beingadded to VC.A load slice is a horizontal strip cut from a load-duration curve (see Chapter 1-4.1). Depending on itsaverage duration it will be served by some particulartechnology, baseload, midload, or peaking. Any givenload slice is defined by a capacity, Kslice, which is theheight of the slice, and an average duration, D. It alsohas a total energy requirement, E =D Kslice. To serveFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.38 PART 1 Power Market Fundamentals8. See DOE (1998a) Tables 1417. In a table of cost characteristics of new generating technologies (DOE2001a, Table 43) OC is given, but not FC. In a slide labeled Electricity Generation Costs, DOE (2001b)reports the capital costs in mills/kWh. As the title indicates, these are FC'cf , for cf determined bytechnology-based capacity factors, and so are components of ACK, as advertised in the title and thus pointson the hyperbolic screening function.this load, generation capacity of Kslice must be installed and must run with a capacityfactor of cf =D. Having selected a technology, one can compute the average costper MW-of-capacity of serving the load, ACK, and the average cost per MWh-of-energy of serving the load, ACE. The total cost of serving load is then given by bothKsliceACK and E ACE. Because Kslice and E are both fixed, choosing the technol-ogy that minimizes either ACK or ACE will minimize the total cost of energy. Thisis why either the traditional or the hyperbolic screening curves can be used.These relationships can be summarized as follows. For a particular load sliceserved by generators with fixed cost, FC, and variable cost, VC, the average costof capacity and energy can be found as follows:Capacity: ACK=FC +cf VC =FC +DVC (1-3.1)Energy: ACE=FC'cf +VC =FC'D +VC (1-3.2)The capacity factor of the generator, cf , equals the average duration of the load, D.No one uses hyperbolic screening curves, but when an average cost is computedfor a specific technology, say by DOE, a value for ACE (not ACK) is always com-puted. Typically, DOE might report the overnight cost (OC), some informationabout fuel costs, and a value for ACE based on technical capacity factor (cf ).8 Inother words, DOE reports some technologically determined value on the technol-ogys hyperbolic screening curve.ACK is used to determine the optimal durations of various generation technolo-gies, and from these durations the optimal investment in these technologies. Sincecompetitive markets optimize technology, ACK is also used to determine competitiveoutcomes. Either ACE or ACK may be used to compare the cost of peak energy withthe value of lost load, depending on whether peaker costs are equated to the valueof lost load or the average hourly cost of lost load (see Chapter 2-2 and 2-3). ACEis also well suited to DOEs interest in alternative technologiesnuclear, wind,solar, and so on. These have in common capacity factors which, even in a marketenvironment, are not affected by normal variations in market structure but areinstead technologically determined because their variable costs are almost alwaysbelow the market price. They run whenever they are physically able, so theircapacity factor is determined by their technical capability. The economics of analternative technology can be assessed by comparing its ACE with the marketsaverage price.Standard technology generators have capacity factors determined by the marketand not just by their technology. In this case, the duration of the load they serve,which determines their capacity factor, needs to be determined from their fixedand variable costs along with those of other technologies. This is done with screen-ing curve analysis, or with algebra based on screening curves. Traditional linearscreening curves prove simplest. These curves and their associated algebra willbe used throughout the book, as is the formula for ACE.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-3 Pricing Power, Energy, and Capacity 39Table 1-3.2 Fixed and Variable Cost of GenerationType of GeneratorOvernightCapacity Cost$/kWFixedCost$/MWhFuelCost$/MBtuHeat rateBtu/kWh VariableCost $/MWhAdvanced nuclear 1729 23.88 0.40 10,400 4.16Coal 1021 14.10 1.25 9,419 11.77Wind 919 13.85 0Advanced combined cycle 533 7.36 3.00 6,927 20.78Combustion turbine 315 4.75 3.00 11,467 34.40 * Overnight capacity cost and heat rates are fromDOE (2001a), Table 43. Plants not labeled advanced are conventional. Rental capacitycosts are computed fromovernight costs, a discount rate of 12% and assumed plant lifetimes of 40 years except for wind and gas turbines whichare assumed to be 20 years. For simplicity, operation and maintenance costs are ignored.1-3.4 TECHNICAL SUPPLEMENTChecking Fixed-Cost Units with the Amortization FormulaAs a final check on the units of fixed costs, the amortization formula can beanalyzed. Interest rates (e.g., 10% per year) has the dimension of per unit time,and T has the dimension of time, so rT is dimensionless, that is, a pure number.This is necessary for compatibility with 1 in the denominator. In the numerator,OC has the traditional units of $/kW and r again has the dimension of 1'time,so r OC has the dimensions of OC per unit time, for example, $/kW per year.If overnight cost is measured in $/kW and interest is given in percent per year, fixedcost must be measured in $/kWy.Fixed and Variable Costs for Different TechnologiesTable 1-3.1 computes fixed and variable costs for five types of generators as anexample of converting overnight cost to fixed costs. The listed values of FC andVC are exactly the values needed to draw screening curves and choose the mostefficient plant to serve loads of any duration. For example, the cost of serving loadof duration D with an advanced combined-cycle plant isACK=(7.36+20.78D) $/MWh.To convert this to the more traditional units of $/kWy, both values should bemultiplied by (1 M'1000 k)(8760 h/y) or 8.76. (Note that, including units, thisis just multiplication by 1 since 1 M =1000 k and 8760 h =1 y.)To avoid having ACK appear to have the same units as variable costs, its unitsare often stated as $/kW per year which translates to $/kW/year. But just as, so $/kW/year equals $/kW-year which is denoted by $/kWy. x'y'z =x'(y z)The phrase $/kW per year is correct, but it means no more and no less than$/kWy, which has the dimensions of dollars per energy.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.And when theRain has wet theKiteand Twine, so that it can conduct theElectric Firefreely,you will find it stream out plentifully from theKey on theApproach of your Knuckle.Benjamin Franklin1752Chapter 1-4Power Supply and DemandTHE PHYSICAL ASPECTS OF SUPPLY AND DEMAND PLAY A PROMINENTROLE IN POWER MARKETS. Shifts in demand, not associated with price, playa role in all markets, but in power markets they often receive attention to theexclusion of price. This is not simply the result of regulatory pricing; even withmarket prices, demand shifts will play a key role in determining the mix of produc-tion technologies. In this way hourly demand fluctuations determine key long-runcharacteristics of supply.Because electric power cannot be stored, production always equals consumption,so the difference between supply and demand cannot be indicated by flows ofpower. Neither is the instantaneous difference indicated by contracts since real-timedemand is determined by customers physically taking power. The short-runsupplydemand balance is indicated by voltage and, especially, frequency. Thisunusual market structure requires some elementary background in system physics.More detail is provided in Chapters 5-1 and 5-2.Chapter Summary 1-4: Load duration curves are still relevant in unregulatedmarkets, but their role in analysis is more subtle because their shape is affectedby price and its correlation with load. They can still be used with screening curvesto check an equilibrium, but to predict an equilibrium they must be used in combina-tion with price elasticity.Power production always equals consumption (counting losses as part ofconsumption) which makes it impossible to assess the supplydemand balance byobserving quantities or quantity flows. Instead, frequency is the proper indicatorof system-wide balance, and net unscheduled flows between regions are used toshare the responsibility of maintaining this balance.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-4 Power Supply and Demand 41Section 1: Describing the Demand for Power. A years worth of hourlyfluctuations can be usefully summarized by a load-duration curve that plots demandagainst duration, the fraction of the year during which demand is at or above acertain level. It can also be thought of as the probability of finding load above acertain level.If customers are charged real-time prices, peak demand will be reduced, allowinga reduction in generating capacity. The result will be a load-duration curve withits peak cut off horizontally.Section 2: Screening Curves and Long-Run Equilibrium. If the screeningcurves of the available technologies are drawn on the same graph, their intersectionsdetermine capacity factors that mark technology boundaries. By mapping thesecapacity factors to durations and then to the load-duration curve, the optimalcapacities for these technologies can be read off the vertical axis.This technique can be used to partially confirm a market equilibrium but notto find one. In a market, price affects the shape of the load-duration curve, so itcannot be taken as given until the equilibrium is known.Section 3: Frequency, Voltage, and Clearing the Market. When consumersturn on ten 100-W light bulbs, they are demanding 1000 W of power, and ifgenerators supply only 900 W, the system will not be in balance. In spite of this,the power supplied will exactly equal the power consumed (ignoring losses). Thisequality of power flows is caused by a decrease in voltage sufficient to cause the100 W bulbs to use only 90 W of power. For motors the same effect is caused bya drop in frequency. Because voltage is automatically adjusted at substations,frequency is the main balancer of power inflows and outflows.The United States is divided into three AC interconnections: the Western,Eastern, and Texas. The system frequency is constant throughout each AC intercon-nection, which means that a change in frequency cannot be used to locate asupplydemand imbalance. Instead, net power flows are tracked out of each controlarea and compared with scheduled power flows. This allows the imbalance to belocated.1-4.1 DESCRIBING THE DEMAND FOR POWERTraditionally the demand for power has been described by a load-duration curvethat measures the number of hours per year the total load is at or above any givenlevel of demand. An example is shown in Figure 1-4.1. Total demand (load) is ademand for a flow of power and is measured in MW. Although the load-durationcurve describes completely the total time spent at each load level, it does not includeinformation about the sequence of these levels. The same load-duration curve canFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.42 PART 1 Power Market Fundamentals1. Service industries such as restaurants and airlines often have demand fluctuations which cause similarproblembecause their output is not storable, but they tend to use the same technology on and off peak.Figure 1-4.1A load-duration curve.be produced by wide daily swings in demand and little seasonal variation or bywide seasonal variation and limited daily swings.The introduction of a market adds the dimension of price. Economists oftenrepresent demand by a demand curve which expresses demand solely as a functionof price. Nonprice fluctuations of the type captured by a load-duration curve arereferred to as shifts in the demand curve and are generally not described in detail.But electricity is different because it is not storable, so peak demand must besatisfied by production from generators that are used as little as 1% of the time.Such generators, peakers, are built with technology that differs markedly fromthat used for baseload generators which run most of the time and are stopped onlyrarely. As a result, power markets face the problem of determining how muchgeneration capacity should be built using each type of technology, for example,coal-fire steam turbines or gas-fired combustion turbines (gas turbines). Thisexplains the unusual importance of demand shifts and consequently of load-durationcurves in power markets.1Load-Duration CurvesA load-duration curve can be constructed for a given region (or for any collectionof loads) by measuring the total load at hourly intervals for each of the 8760 hoursin a year, sorting them, and graphing them starting with the highest load. The resultis a curve that slopes downward from the maximum load in the peak hour, hour1, to the minimum load, baseload, in the most off-peak hour, hour 8760 (see Figure1-4.1).Duration is traditionally measured in hours per year, but both hours and yearsare measures of time, so duration is dimensionless, which means it can be expressedas a pure number, a ratio, or percentage. To convert from units of hours per year(h/year) to a pure number, simply multiply by 1 in the form (1 year)'(8760 h).Duration has a natural interpretation as the probability that load will be at or abovea certain level. To use this interpretation pick a load level, say 35 GW, and usingthe load-duration curve, find the corresponding duration, 20% in this case. ThisFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-4 Power Supply and Demand 432. There is no natural definition of short- and long-run demand elasticity, which can be defined usefullyover any time horizon fromfive minutes to twenty years. This text will use short-run elasticity to meansomething on the order of one day and long-run to mean about five years.indicates that load is 35 GW or greater 20% of the time. Put another way, theprobability of load being 35 GW or greater in a randomly selected hour is 20%.This interpretation is most convenient.The Price-Elasticity of DemandPresently, demand is almost completely unresponsive to price in most powermarkets because wholesale price fluctuations are not usually passed on to retailcustomers. Often retail prices remain under some form of price regulation, butcompetitive retailers have also been slow to implement real-time pricing. In thelonger run, retail prices do change, sometimes seasonally. In the long run a 10%increase in the price of power will cause approximately a 10% reduction in the useof power.2 This is not a very accurate approximation, but the long-run responseto a 10% increase in price is likely to be found between 5% and 15% and is certainlynot zero. Economists term this price sensitivity a price elasticity of demand, whichis often shortened to demand elasticity. If a 10% change in price causes a 5%, 10%,or 15% change in demand, the elasticity is said to be 0.5, 1.0, or 1.5, respectively.(Technically, demand elasticities are negative, but this book will follow the commonconvention of re-defining them to be positive.)Real-Time Pricing and the Load-Duration CurveUnder regulation, residential load usually faces a price that fluctuates very littlewhile commercial and industrial load often face time-of-use (TOU) pricing ordemand charges. Time-of-use prices are designed to be high when demand is high,but the approximation is crude as they are set years in advance. Consequently theymiss the crucial weather-driven demand fluctuations that cause most problematicsupply shortages. Demand charges are no more accurate as they are based onindividual demand peaks, not system peaks. Coincident-peak charges improve onthis by charging customers for their use at the time of the system peak, but theseare less common.Because supply is fairly constant, the market is tightest when demand is highest.Consequently, high wholesale prices correspond well with high demand. If thesereal-time prices are passed through to customers, then retail prices will track loadfairly well. Although real-time prices work best, all four pricing techniques, TOU,demand, coincident-peak, and real-time, tend to raise prices when demand is highestand reduce prices when demand is lowest. This results in lowering the peak of theload-duration curve and raising the low end of the curve.If load faced real-time prices, the need for generation capacity might be reducedto the point where the load-duration curve under regulation had a duration of, say,10%. Then, between 0% and 10% duration, supply and demand would be balancedby price. Instead of having generation follow load, load would be held constantby price at the level of installed capacity. In the lowest duration hours, price wouldFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.44 PART 1 Power Market FundamentalsFigure 1-4.2The effect of priceelasticity on loadduration.need to be very high to reduce demand to this level. By fluctuating sufficiently,price would control demand and produce a flat-topped load-duration curve witha maximum load just equal to generating capacity as shown in Figure 1-4.2.1-4.2 SCREENING CURVES AND LONG-RUN EQUILIBRIUMWhen demand is inelastic or when it faces a fixed price so that the load-durationcurve is fixed, this curve can be used to find the optimal mix of generation technolo-gies. The technique was developed for a regulated power system in which priceand the load-duration curve are often fixed, but it is still useful for understandingcertain aspects of competitive markets.It assumes that fixed and variable costs adequately describe generators. Theseare used to draw screening curves for each technology on a single graph as shownin Figure 1-4.3. The intersections of these curves determine capacity factors thatseparate the regions in which the different technologies are optimal. These capacityfactors equal the load durations that determine the boundaries between load thatis served by one technology and the next. The screening curves in the figure aretaken fromFigure 1-3.1 and intersect at a capacity factor, cf , of approximately 30%.Consequently all load with a duration greater than 30%, or about 2600 hours, shouldbe served by coal plants, while load of lesser duration should be served by gasturbines. The arrow in the figure shows how the needed capacity of coal plantscan be read from the load-duration curve. The optimal GT capacity is found bysubtracting this from maximum load which is the total necessary capacity. (Forcedoutages and operating reserve margins are considered in Parts 2 and 3.)If customers face the wholesale market price through real-time pricing, thistechnique cannot be used because the load-duration curve depends on price, andprice depends on the choice of technology, and the choice of technology depends,as just described, on the load-duration curve. This circularity is in no way contradic-tory, but it makes it difficult to find the competitive market equilibrium. Not onlyis calculation more difficult, but, also, the elasticity of demand must be known.In spite of this circularity, the traditional technique can be used to partiallyconfirm a long-run equilibrium. The load-duration curve observed in a marketFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-4 Power Supply and Demand 45Figure 1-4.3Using screening curvesto find the optimal mix oftechnologies.includes the effect of price on demand. When it is used along with the screeningcurves of the available technologies, the traditional method should predict the mixof technologies observed in the market if the market is in long-run equilibrium.In practice many complications must be overcome.1-4.3 FREQUENCY, VOLTAGE, AND CLEARING THE MARKETSo far, this chapter has considered how to describe demand and how to find theoptimal mix of technology to supply it. This section considers the physical detailsof the supplydemand balance in real time. At any instant, customers are usingpower, generators are producing it, and the amount produced is exactly equal tothe amount consumed. Some may object to the word exactly, but the discrepancyis at least a thousand times smaller than anyones ability to measure it and is entirelyirrelevant. The determination of the supplydemand balance depends on electricalphenomena more subtle than the concepts of quantity and quantity flow.LossesIn real networks, a few percent of the power consumed is consumed by the network.This consumption should be considered part of demand even though it serves noend used. With this convention, the system can be viewed as maintaining a perfectbalance between supply and consumption (including losses) at all times and betweensupply and demand whenever customers are getting the power they want.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.46 PART 1 Power Market Fundamentals3. More precisely, the amount stored is minuscule and cannot be utilized for trade.

Convention Loss Provision is Not Considered Part of Supply or Demand Losses will be considered as a service paid for by traders and provided separatelyfrom the trading arrangement. Consequently, from a trading point of view, powerflows can be viewed as lossless.Supply precisely equals consumption because there is no storage of power intransmission systems.3 But if supply equals consumption regardless of price, whatsignal should be used for price adjustment? How can demand be observed to beeither greater than or less than supply? A mismatch between supply and demandis signaled not by power flows but by frequency and voltage. When they are belowtheir target values, demand exceeds supply and vice versa.Frequency and VoltagePower systems attempt to maintain a constant frequency, the rate at which alternat-ing current alternates. In the United States, alternating current (AC) reversesdirection twice, thus completing one cycle and returning to its original direction,60 times per second. The frequency of AC in the United States is therefore saidto be 60 cycles per second, also known as 60 Hertz or 60 Hz. In many countriesthe target frequency is 50 Hz.Voltage is the amount of electrical pressure that pushes current through electricalappliances such as lights and motors. As with frequency, power systems have acertain target voltage that they attempt to maintain. In the United States the targetresidential voltage is about 120 volts. In some countries the target voltage is abouttwice as high. When an unprotected 120-V appliance is plugged into a 240-V outlet,the extra electrical pressure (voltage) causes twice as much current to flow throughthe appliance. This causes the appliance to use four times as much power (poweris voltage times current) and the appliance typically burns out. The important pointfor this section is that as voltage increases, most appliances use more power, andas voltage decreases most appliances use less power.Imagine a system with ten generators operating at full throttle supplying tenthousand homes with lights burning and motors running. If one generator goes offline, two things happen. The system voltage and frequence both decrease. Bothcause electrical appliances to use less power. This effect has been described forvoltage, but for more complex reasons most motors use less power when the systemfrequency declines. The decline in voltage and frequency is produced automaticallyby the physics of the entire system including all loads and generators. It happensto the exact extent necessary to balance inflow (supply) and outflow (consumption).If this did not happen, a law of physics, just as fundamental as the law of gravity,would be violated.Although nothing can prevent the combined drop in frequency and voltage whengeneration is reduced and load maintained, it is possible to influence the relativeextent to which each decreases. In fact, the system has automatic controls that doFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-4 Power Supply and Demand 474. If the frequency difference between Maine and Florida were 0.001 Hz, for one minute, it would causean accumulated phase change between the two states of 22 degrees. This would lead to dramatic changesin power flow. Thus while the frequency lock between utilities is not exact, it is extremely tight, and therecan be no persistent frequency difference. One utility cannot have a problemunless they all do.just that. At substations, where very high transmission voltages are reduced to thelower, but still high, distribution voltage, there are automatically controlled trans-formers. These adjust so that the distribution voltage remains relatively constanteven when the transmission voltage drops. Because of these devices, more of thepower flow adjustment that accompanies the loss of a generator is accomplishedthrough frequency reduction than through voltage reduction. Nonetheless both canand do happen.Frequency and InterconnectionsAn interconnection is a portion of the power grid connected by AC power lines.The three interconnections in the United Statesthe Eastern Interconnection,the Western Interconnection, and most of the Great State of Texaseach maintaina uniformfrequency. Frequencies in Maine and Texas bear no particular relationshipto each other, but the AC voltage in Maine stays right in step with the AC voltagein Florida, night and day, year in and year out. The frequency in every utility inan entire interconnection is exactly the same.4 If one utility has a problem, theyall have a problem.These three interconnections are connected to each other by a number of smalllines, but they are separate interconnections because the connecting lines are allDC lines. No AC power flows between them. On DC lines, the electrical currentflows in only one direction; it does not alternate directions. Thus DC lines haveno frequency and as a consequence need not (and cannot) be synchronized withthe power flow of an AC interconnection. This allows trade between two differentinterconnections that are not synchronized with each other.The Signal for Price AdjustmentWhen a generator breaks down unexpectedly (a forced outage) and supply de-creases, demand is then greater than supply, even though consumption still preciselyequals supply. Consumption is less than demand because of rationing. A consumerwith a 100-W light turned on is demanding 100 watts of power. During a brownout, however, 100 watts are not supplied to the bulb as power to the bulb is rationedby the suppliers. This rationing is not due to deliberate action but is a consequenceof system physics which automatically lowers the voltage and frequency. Forsimplicity, in the remainder of this section, rationing will be discussed as if ithappened solely through frequency reduction, as this is generally considered tobe the predominant effect.A drop in frequency below the target level of 60 Hz is a clear and accurateindication that demand exceeds supply for the interconnection as a whole. Similarly,any frequency above 60 Hz indicates that supply exceeds demand. In other words,more than 100 watts are being delivered to 100-W motors. This extra power isFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.48 PART 1 Power Market Fundamentalsgenerally unwanted because appliances are built and operated on the assumptionthat power will be delivered at a frequency of 60 Hz.Because frequency indicates the discrepancies between supply and demand,frequency is the right guide for interconnection-wide price adjustment. Whenfrequency is high, price should be reduced; when frequency is low, price shouldbe raised. This is the classic adjustment process for keeping supply equal to demand.

Definition DemandThe demand for power is the amount of power that would be consumed if systemfrequency and voltage were equal to their target values for all consumers. Notethat shed load is included as part of demand. This is an economic definition andcontradicts the engineering definition provided by North American ElectricReliability Council (NERC). (Often load is used to mean demand.)

Result 1-4.1 Supply Equals Consumption but May Not Equal DemandAs in all markets, demand is the amount customers would buy at the market pricewere supply available. If voltage or frequency is low, customers consume lesspower than they would like so supply is less than demand.As always, the real world adds one more layer of complexity. The frequencyin every power market in an interconnection is exactly the same. Thus frequencyreveals nothing about the supply and demand conditions in any particular marketbut only about the aggregate supply and demand conditions of the entire intercon-nection. Consequently individual markets cannot rely on the frequency alone todetermine their price adjustments.NERC defines another control variable that takes account of both frequencyand the net excess flow out of a trading region (the net interchange). The net excessoutflow is the actual outflow minus the scheduled outflow. An excess outflow isa strong signal that supply is greater than demand in the trading region. If thefrequency is high in the interconnection this is a weak signal of excess supply inany particular market. These two signals are combined to form a single indicatorof excess supply for each market. The indicator is called the area control error, orACE. Control areas are required to keep their ACE near zero, and they do. ACEis the main indicator of the supplydemand balance in every control area in theUnited States and when there is a market, it is the signal that determines whetherthe price will be increased or decreased by the system operator.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Therich, . . . in spiteof their natural selfishness and rapacity, . . . though thesoleend which theypropose. . . bethegratification of their own vain and insatiabledesires, they dividewith thepoortheproduceof all their improvements. They areled by an invisiblehand to makenearly thesamedistribution of thenecessaries of life, which would havebeen made, had theearth been dividedinto equal portions among all its inhabitants, and thus without intending it, without knowingit, advancetheinterest of thesociety.Adam SmithTheTheory of Moral Sentiments1759Chapter 1-5What Is Competition?COMPETITION IS LEAST POPULAR WITH THE COMPETITORS. Everysupplier wants to raise the market price, just as every buyer wants to lower it.Perfect competition frustrates both intentions.Some commodity markets provide almost perfect competition; eventually powermarkets may work almost as well. But designing such markets is difficult. Economiccompetition is not like competition in sports, which may be considered perfect whenthere are just two powerful and equal competitors. Economists consider competitionto be perfect when every competitor is small enough (atomistic is the term used)to have no discernable influence against the invisible hand of the market.Adam Smith guessed intuitively that a perfectly competitive market, in theeconomic sense, would produce an outcome that is in some way ideal. Manydifficulties can cause a market to fall short of this ideal, but even a market that isonly workably competitive can provide a powerful force for efficiency andinnovation.Power markets should be designed to be as competitive as possible but thatrequires an understanding of how competition works and what interferes with it.On its surface, competition is a simple process driven, as Adam Smith noted, byselfishness and rapacity; but the invisible hand works in subtle ways that are oftenmisunderstood. Those unfamiliar with these subtleties often conclude that suppliersare either going broke or making a fortune. This chapter explains the mechanismsthat keep supply and demand in balance while coordinating production and con-sumption to produce the promised efficient outcome.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.50 PART 1 Power Market FundamentalsChapter Summary 1-5: The plan of deregulation is to achieve efficiencythrough competition. Economics guarantees this result provided the market reachesa classic competitive equilibrium. This requires at least three conditions to be met:price taking suppliers, public knowledge of the market price, and well-behavedproduction costs. Although production costs seem problematic to many, they causelittle trouble, and deregulation will probably succeed if markets are designed formaximum competition and transparent prices.Section 1: Competition Means More than Struggle. The dictionary definescompetition as a struggle with others for victory or supremacy, but economicsdoes not. Designing markets to be competitive in the dictionarys sports-orientedsense produces poor designs about which little can be predicted. Economic competi-tion requires many competitors on each side of the market and results in a lack ofmarket power and price taking behavior.Section 2: Efficient Markets and the Invisible Hand. The central resultof economics states that competition leads to efficiency. But to achieve short-runefficiency, competitive behavior must be supplemented with well-behaved costsand good information. Long-run efficiency requires free-entry of new competitorsas well. Efficiency means that total surplus, the sum of profit and consumer surplus,is maximized.Section 3: Short- and Long-Run Equilibrium Dynamics. Price and quantityadjustments, usually by suppliers, lead the market to equilibrium. In a competitivemarket, suppliers adjust output until marginal cost equals the market price and adjustprice until the market clears (supply equals demand). They are price takers becausewhen considering what quantity to produce they take the market price as given;that is, they assume it will remain unchanged if they change their output. A long-run competitive equilibriumis brought about by investment in productivecapacity. Profit (which means long-run economic profit) is revenue minus costs,and cost includes a normal return on capital (investment). Thus, zero economicprofit provides a normal return on investment. If economic profit is positive andthe market competitive, new suppliers will enter. In this way profit is brought downto zero under competition, but this is enough to cover all fixed costs and a normalrisk premium.Section 4: Why is Competition Good for Consumers? Competition mini-mizes long-run costs and pays suppliers only enough to cover these minimum costs.Although it is possible to depress price in the short run, it is not possible to payless on average than minimum long-run average cost.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-5 What Is Competition? 511. Under the special and uncommon conditions of Bertrand competition, two competitors are enough.1-5.1 COMPETITION MEANS MORE THAN STRUGGLEThe dictionary defines competition as a struggle with others for victory or suprem-acy. This definition is based on sports, not economics, but is quite influential withregulators and politicians. Consequently, when economics says competition isdesirable, this is often interpreted to mean that struggle among market playersis desirable. There is a grain of truth to this interpretation, but it misses the mainpoint.The popular view judges competition mainly on fairness, so market power onthe supply side is not a problem provided that demand is similarly endowed.Competition is now in vogue with many regulators, and many who have spent alifetime passing judgment on the fairness of prices have taken up the call to letthe market do it. They see their new job as making sure the new markets are fair,that the playing field is level. They believe it is only necessary to ensure thestruggle between market players is fair. Because economics promises that competi-tive markets will be efficient, a good outcome is thought to be assured.The economic promise of efficiency is not predicated on a fair struggle. Twofairly matched competitors do not approximate what economics means bycompetition. For example, economics makes no guarantee that pitting a monopolytransco against an equally powerful load aggregator will produce an even moder-ately acceptable outcome. Economics cannot predict the outcome of this kind ofcompetition and would view this as a very poorly structured market.The economists notion of competition refers to competition among suppliersor among demanders but not between suppliers and demanders. Competition isnot a struggle between those who want a higher price and those who want a lowerprice. The process of economic competition between many small suppliers worksby suppliers undercutting each others price in order to take away the otherscustomers. This drives the price down to the marginal cost of production but nolower because at lower prices suppliers would lose money. If supply-side competi-tion is stiff enough, the market price will be pinned to the marginal-cost floor. Thisis the meaning of perfect competition.When suppliers face such stiff competition that they cannot affect the marketprice and must simply accept it and sell all they can sell profitably at this price,they are said to be price takers. This is the principle requirement for a market tobe perfectly competitive and is the primary assumption on which economic claimsof market efficiency rest. Generally it takes many competitors, none of which have a large market share,to produce perfect competition in the economic sense.1 If there are any largesuppliers they are likely to have the ability to profitably raise price. In this casethey are not price takers and are said to have market power. They know they canaffect the supplydemand balance by reducing their output and thereby drive upthe price enough to increase their profit.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.52 PART 1 Power Market Fundamentals2. Smith is often quoted as saying that a market is guided as if by an invisible hand. But a full textsearch of The Wealth of Nations reveals only this one use of invisible hand. In the same year Smithsbook was published, George Washington observed, in his first inaugural address that the Invisible Hand(of God) had guided the United States to victory. In fact, both Smith and Washington viewed the invisiblehand, God, and the forces of nature as being nearly synonymous.3. Economists do not get authentic Nobel prizes. The prize in economics is given by the Bank of Sweden,not by the Nobel Foundation.4. This discussion is necessarily far fromrigorous and is meant only to convey a general understandingof the most important concepts. See Mas-Colell et al. (1995) starting on p. 308.1-5.2 THE EFFICIENCY OF PERFECT COMPETITIONOne economic result is, without doubt, the most prominent in all of economics.It is the point made by Adam Smith in the Wealth of Nations:... he intends only his own gain, and he is in this, as in many othercases, led by an invisible hand to promote an end which was nopart of his intention.2Vague as this may be, Adam Smith, and later Leon Walras, are correctly creditedwith developing the notion that competitive markets harness the profit motive toproduce an efficient and socially useful outcome. This Efficient-Competition Resulthas been re-examined many times and modern proofs have resulted in NobelPrizes for Kenneth Arrow (1972) and Gerard Debreu in (1983).3Short-Run CompetitionThe Efficient-Competition Result has limitations. It does not mean that every freemarket is efficient, or even that every free market in which suppliers are price takersis efficient. Because of these limitations, economics has carefully defined bothcompetition and efficiency and has added two more concepts: well-behaved costfunctions and good information. The modern Efficient-Competition Result canbe summarized as follows:

This result can also be summarized as a competitive equilibrium is efficient.4The three conditions listed above under competition, are necessary to guaranteethat the market will reach a competitive equilibrium. If suppliers have smallenough market shares, they will not have the power to change the market price andprofit fromdoing so, and they will take price as given. This is called acting competi-tively, but it does not guarantee a competitive equilibrium. First, such an equilibriummust exist and second, traders must be able to find it. If costs are not well be-havedand startup and no-load costs are notthere will be no equilibrium. Iftraders lack adequate information, including publicly known prices, they may notFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-5 What Is Competition? 535. See Mas-Colell et al. (1995, 334). 6. The termallocative efficiency is almost universally used to mean demand-side efficiency. But thisis not the meaning found in economics dictionaries; which include both sides of the market and do notdistinguish it fromefficiency.find the competitive equilibrium which consists of an optimal set of trades. (Prob-lems with ill-behaved, nonconvex, costs and lack of information are discussed inChapter 3-8.)

Definitions Perfect CompetitionAgents act competitively, have well-behaved costs and good information, and freeentry is brings the economic profit level to zero.Act CompetitivelyTo take the market price as given (be a price taker).Well-Behaved CostsShort-run marginal cost increases with output and the average cost of productionstops decreasing when a suppliers size reaches a moderate level.Good InformationMarket prices are publicly known.Long-Run CompetitionA short-run competitive equilibrium is (short-run) efficient; it makes the best useof presently available productive resources. A long-run competitive equilibriumguarantees that the right investments in productive capacity have been made butrequires that the three short-run conditions be met and adds two new ones. Produc-tion costs must not possess the conditions for a natural monopoly (see Section 1-1.1), and competitors must be able to enter the market freely.5 With free entry,if there are above-normal profits to be made, new suppliers will enter which willreduce the level of profits. In this way free entry ensures that profits will not beabove normal. A normal profit level is the key characteristic of a long-run competi-tive equilibrium. Barriers to entry is the term used to describe market characteris-tics that prevent free entry.Efficiency and Total SurplusAlmost every proposed market design is declared efficient, but in economics theterm has a specific meaning. The simplest meaning applies to productive efficiencywhich means that what is being produced is being produced at the least possiblecost. Minimizing cost is often the most difficult part of the market designersproblem, so this meaning is generally sufficient.When not qualified as productive efficiency, efficiency includes both the supplyand demand sides of the market.6 Efficiency means (1) the output is produced bythe cheapest suppliers, (2) it is consumed by those most willing to pay for it, and(3) the right amount is produced. These three can be combined into a single criterionby using the concept of consumer surplus.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.54 PART 1 Power Market FundamentalsFigure 1-5.2Total surplus equals thearea between the demandcurve and the marginalcost curve.The Efficient-Competition Result

Definitions Productive EfficiencyProduction costs have been minimized given total production.EfficiencyTotal surplus has been maximized. This automatically includes minimizing thecost of what is produced and maximizing the value of what is consumed, as wellas producing and consuming the right amount.A consumers demand curve measures how much the consumer would pay forthe first kilowatt-hour consumed, and the second, and so on. Generally the moreconsumed, the less would be paid for the next kilowatt-hour. Because the initialkilowatt-hours are so valuable, the total value of consumption is generally muchgreater than the amount paid. The difference between the maximum a consumerwould pay as revealed by the consumers demand curve and what the consumeractually does pay is the consumers surplus.Profit is analogous to consumer surplus and is often called producer surplus.It is total revenue minus total cost, while consumer surplus is total value to consum-ers, V, minus total consumer cost, CC. (V is sometimes called gross consumersurplus, and is the area under the demand curve for all consumption.) Both V andCC are measured in dollars. If the sumof profit and consumer surplus is maximized,the market is efficient, and all three of the above criteria follow. When profit (R !! C) and consumer surplus are added, the consumer (V !! CC)costs (CC) and producer revenue (R) cancel because they are the same. The resultis total surplus (V !! C), consumer value minus producer cost. Consequentlyefficiency is the same as maximizing total surplus.

Result 1-5.1 Competitive Prices Are Short- and Long-Run EfficientIf productions costs are well behaved so competitive prices exist, these prices willinduce short-run (dispatch) efficiency and long-run (investment) efficiency.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-5 What Is Competition? 55Note that the Efficient-Competition Result does not say that a markets prices willbe competitive if costs are well behaved. That conclusion requires the lack of marketpower and good information. The Efficient-Competition Result says that if marketprices are competitive then supply and demand will be efficient. Assuring competi-tive prices is the main problem addressed by this book.Problems Caused by Production CostsThe Efficient-Competition Result depends on well-behaved production costs andthese cannot be designed. Either efficient generators have well-behaved costs orthey do not. If they do not, and costs are sufficiently problematic, then a standardcompetitive market design cannot be depended on to provide an efficient outcome.Cost problems present the most fundamental challenge. Three different problemsreceive attention: (1) nonconvex operating costs, (2) the fixed costs of investment,and (3) total production costs that decrease up to very large scales of production.The third problemis the problem of natural monopoly and was discussed in Chapter1-1.The second problem is the subject of the most frequent misconception, anextremely pessimistic one. It holds that ordinary fixed costs are sufficient to disrupta competitive market. This pessimism about competition is often accompanied byoptimism about less-competitive free markets. The belief is that if the market canavoid the problems of a competitive equilibrium free-market forces will producea good outcome. Perhaps, it is argued, if the market is not monitored too closely,generators will exercise market power and thereby earn enough to cover fixed costsand keep themselves in business. Chapter 2-1 shows that fixed costs are not aproblem for competition and the proposed noncompetitive remedy is unnecessaryand detrimental.The problem of nonconvex operating costs is the most difficult. The cost ofstarting a generator makes generation costs nonconvex because it makes it cheaperper kWh to produce 2 kWh than to produce 1kWh. This causes the market to lacka competitive equilibrium and could easily cause inefficiency in the dispatch ofan otherwise competitive market. To circumvent this problem, some markets usea unit-commitment auction that attempts to replace a standard classic competitiveequilibrium with a different equilibrium which is still efficient. Chapter 3-9 dis-cusses this problem in detail and suggests it may be of minor importance and thata standard competitive market might still provide a very high level of efficiency.These conclusions are part of a larger pattern. Competitive markets are difficultto design, and none of the three basic requirements of efficiency can be achievedto perfection. But if the two controllable ones, price taking behavior and goodinformation, are well approximated, a very efficient market will result. The quirksof a competitive equilibriumare not much of a problem, but designing a competitivemarket requires a great deal of care.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.56 PART 1 Power Market Fundamentals7. Demand-side management concerns itself primarily with information problems on the demand side ofthe market. These problems also deserve attention.8. For a more complete treatment of the microeconomics of competition presented with power marketsin mind, see Rothwell and Gomez (2002).The Meaning ofShort Run and Long RunThese concepts do not, as is often supposed, referto specific periods of time but instead refer to thecompletion of particular market adjustment pro-cesses. In the short run indicates that adjustmentsin the capital stock (the collection of power plants)are being ignored, but adjustments in the output ofexisting plants are being considered.The phrase in the long run indicates adjustmentsin the capital stock are not only being considered butare assumed to have come to completion. This is auseful abstraction. If the market has not recentlysuffered an unexpected shock, it should be near astate of long-run equilibrium because businessspends a great deal of effort attempting to discernfuture conditions, and for the last five years, todaywas the future.Of course mistakes are made and markets arenever in exact long-run equilibrium. But mistakes areas often optimistic as pessimistic, and consequentlya long-run analysis is about right on average. How-ever, a newly-created market is more likely thanmost to be far from its equilibrium.1-5.3 SHORT- AND LONG-RUN EQUILIBRIUM DYNAMICS Markets are never in equilibrium, but economics focuses primarily on their equilib-rium behavior. The ocean is never in equilibrium, yet it is always found at the lowestelevations where physics predicts its equilibrium to be. In equilibrium the oceanwould have no waves. Although markets, like oceans, have waves, they toousually stay near their equilibrium. An equilibrium may change over time as theglobe warms and the ice caps melt, but this does not prove the equilibrium uninter-esting. A markets equilibrium is a useful guide to its behavior, even though themarket is never exactly in equilibrium.Both the supply and the demand side of the marketadjust their behavior in order to produce a marketequilibrium, but competitive economics is primarilyconcerned with the supply side.7 This section exploresthe forces that push the supply side of a market towarda competitive equilibrium.8The Short-Run EquilibriumMarginal cost is the cost of producing one more unitof output, one more kilowatt-hour. It is also approxi-mately the savings from producing one less kWh. Inthis section and the next, these are assumed to be soclose together that no distinction is necessary, whichis typically the case. Chapter 1-6 pays a great deal ofattention to the special case where these are different.In a competitive market suppliers are price takers.They cannot change the market price profitably, sothey consider it fixed. Price taking also means they cansell all they want at the market price, but they cannotsell anything at a higher price. Most markets are notperfectly competitive, and suppliers find that at ahigher price they sell less but more than nothing. Thiswill be ignored as the present purpose is to analyzehow a market would work if it were perfectly competitive.A short-run competitive equilibrium determines a market price and a marketquantity traded. To bring the market into equilibrium, two dynamic adjustmentmechanisms are needed: (1) a price adjustment and (2) a quantity adjustment. Inmost markets suppliers adjust both, although in some, buyers set the price.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-5 What Is Competition? 57Price Taking and Price AdjustingSuppliers typically name their price. For example,most retailers put price tags on their wares, andcustomers pay those prices. So how can suppliersbe price takers?Because price-taking has a specialized mean-ing, suppliers can be both price takers and priceadjusters at the same time. Suppliers take price asgiven when deciding how much to produce andadjust their price if they notice excess supply ordemand in the market.The Marginal-Cost Pricing ResultQuantity Adjustment. A price taking supplier will increase output if its marginalcost, MC, is less than the market price, P, and will decrease its output if MC >P.Its profit increases by (P !! MC) for every unit produced when P is higher than MCand decreases by (MC !! P) when P is lower.Price Adjustment. Whenever demand exceeds supply, suppliers raise their prices,and whenever supply exceeds demand, they lower prices.Equilibrium. The quantity adjustment dynamic causes the marginal cost to equalthe market price in a competitive market. The price adjustment dynamic causesthe quantity supplied to equal the quantity demanded. When supply equals demand,the market is said to have cleared, and the price that accomplishes this is calledthe market-clearing price, or the equilibrium price, or, for a competitive market,the competitive price. Together the two adjustment mechanisms bring a competitivemarket to a competitive equilibrium.Price Taking vs. Price Adjustment. Notice thatprice taking suppliers adjust their prices in order toclear the market. This is not a contradiction. Pricetaking is something that happens in the quantity-ad-justment dynamic but not in the price-adjustment dy-namic. Price takers take the price as given when com-puting their profit-maximizing output quantity. Thismeans they assume that their choice of output will notaffect the price they receive for it.The quantity dynamic, which causes MC to equalthe market price, acts as a coordinating mechanismamong suppliers because there is only one marketprice. This is why public knowledge of the market price is a key assumption ofthe Efficient-Competition Result. Because all suppliers have the same marginalcost in the competitive equilibrium, no money can be saved by having one producemore and another less. This is what makes production efficient.Some will object to this result on the grounds that coal plants have lowermarginal costs than gas turbines even in a competitive equilibrium. This objectionis based on a misunderstanding of the definition of marginal cost, which willbe explained in the following chapter.

Result 1-5.2 Competitive Suppliers Set Output So That MC =PA competitive producer sets output to the level at which marginal cost equals themarket price, whether or not that is the competitive price. This maximizes profit. (MC =Pfor all suppliers.) February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.58 PART 1 Power Market FundamentalsThe Long-Run EquilibriumThe process of long-run competition involves investing in plant and equipment,not simply changing the output of existing plants. This dynamic requires a definitionof profit. Profit is of course revenue minus cost, but economics defines costs morebroadly than does business. Economics, and this book, define cost to include anormal rate of return on all investment. This rate of return is defined to includea risk premium. If a supplier covers its costs, it automatically earns a normal rateof return, including an appropriate risk premium, on its entire investment. Underthis definition of normal, a business that earns more is considered to be worthinvesting in, and a business that earns less is not. A normal business investment,therefore, has revenues that exactly cover all its costs in the economists sense.Because profit equals revenue minus cost, a normally profitable supplier earnszero profit.

Definition (Economic) ProfitRevenue minus total cost, where total cost includes a normal, risk-adjusted, returnon investment. The normal (economic) profit level is zero. (Business defines anormal return on equity to be profit, while economics defines it as covering thecost of equity.)Short-Run ProfitRevenues minus short-run costs which include variable, startup and no-load costs.The profit function, defined in Chapter 2-7, computes short-run profits.As defined, profit is synonymous with long-run profit which is different fromshort-run profit which does not include the cost of capital; that is, it does not includeany return on investment. Consequently, short-run profit is expected to be positiveon average so these profits can cover the fixed cost of capital.

Result 1-5.3a Under Competition, Average Economic Profit Is ZeroIn a long-run competitive equilibrium, the possibility of entry and exit guaranteesthat profits will be normal, which is to say zero.Result 1-5.3b Under Competition, Fixed Costs Are CoveredWhen profit is zero, all costs are covered including fixed costs, so in the long run,competition guarantees that fixed costs will be covered.Result 1-5.3c A Supplier with a Unique Advantage Can Do BetterIf a supplier has access to limited cheaper inputs (hydro-power or geothermalenergy), it will have greater profits. If the advantage is unlimited, it has a naturalmonopoly.If the expected market price is so low that a supplier cannot enter the marketand cover all costs, no supplier will enter. More specifically, if a new generationunit cannot cover all costs, no new units will be built. The result will be a graduallydiminishing supply of generation (due to retirements of old plants) in the face ofFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-5 What Is Competition? 59gradually increasing demand. This tightening of the market will cause the priceto rise, and eventually price will be high enough to cover all costs. Similarly, if price is so high that costs are more than covered, suppliers willbuild new generating units. This will increase supply and cause the price to fall.The result of this long-run dynamic is that the profit in any competitive marketreturns to the normal level of profit (zero) in the long-run competitive equilibrium.1-5.4 WHY IS COMPETITION GOOD FOR CONSUMERS?In the long-run producers cover their fixed costs, and in the short run total surplusis maximized, but what consumers want is a low price. Does competition providethe lowest possible price?Not in the short run. In the short run, it is possible to design market rules whichlower the market price without reducing supply. This is difficult but possible. Butat a lower price producers will not cover their fixed costs. This will make futureinvestors think twice. The result will be a risk-premium added to the cost of capitaland future production will be more costly than it would have been had cost beenleft at the competitive level.Competition does not guarantee the lowest possible price at any point in time.Instead it guarantees that suppliers will just cover the long-run total costs and nomore. It also guarantees that the cheapest suppliers will be the ones producing.Together these mean production costs (including the long-run cost of investedcapital) are minimized and producers are paid only enough to cover their cost. Thisimplies that the long-run average cost to consumers is also minimized. No marketdesign regulated or unregulated can induce suppliers to sell below cost on average.Competition minimizes long-run average costs of production and long-run averagecosts to consumers.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Thetroublewith theworld is not that peopleknow too little,but that they know so many things that ain't so.Mark Twain(18351910)Chapter 1-6Marginal Cost in a Power MarketSIMPLIFIED DIAGRAMS OF GENERATION SUPPLY CURVES HAVE CON-FUSED THE DISCUSSION OF MARGINAL COST. Typically, these supply curvesare diagrammed to show a constant marginal cost up to the point of maximumgeneration. Then marginal cost becomes infinite without taking on intermediatevalues. Typically it jumps from about $30 to infinity with only an infinitesimalincrease in output. Mathematics calls such a jump a discontinuity. In fact, the curvewould be discontinuous if it jumped only from $30 to $40.The definition of marginal cost does not apply only to the points of discontinuity.Hence it does not apply to a right-angle supply curve at the point of full output,neither does it apply to the points of a market supply curve at which it jumps fromone generators marginal cost to the next. Unfortunately market equilibria sometimesoccur at such points, and concerns over market power often focus on them. Attemptsto apply the standard definition at these points can produce confusing and erroneousresults. Fortunately, the definition is based on mathematics that generalizes naturallyto discontinuous curves. Applying this generalization to the textbook definitionclears up the confusion and restores the economic results that otherwise appearto fail in power markets. For example, in power markets, as in all other markets,the competitive price is never greater than the marginal cost of production.Chapter Summary 1-6: Individual supply curves are often constructed withan abrupt end that causes the market supply curve to have abrupt steps. The standardmarginal-cost definition does not apply at such points. Instead, left- and right-handmarginal costs should be used to define the marginal-cost range. Then the competi-tive price, which remains well defined, will always lie within that range. A marketprice exceeding the marginal-cost range indicates market power.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-6 Marginal Cost in a Power Market 61Section 1: The Role of Marginal Cost. Marginal costs play a key role in cost-based power auctions because they help determine the competitive price. They alsoplay a key role in analyzing market power and gain their importance by definingthe competitive supply curve for individual generators. To find the market (aggre-gate) supply curve, individual supply curves are summed horizontally.Section 2: Marginal-Cost Fallacies. In power-market analysis, marginal costis often defined as the cost of the last unit produced, but this definition is foundin no economics text. A second fallacy asserts that when marginal cost is ambigu-ous, the competitive price is ambiguous. Together these lead to a variety of errone-ous conclusions, such as the competitive price is above marginal cost, and thecompetitive price is ambiguous. Section 3: The Definition of Marginal Cost. When a marginal-cost curveis discontinuous (has a sudden jump), marginal cost can be specified only withina range at the points of discontinuity. This range extends from the left-hand to theright-hand marginal cost at the point under consideration. For all points where thecurve is continuous, the range is a single point equal to the standard marginal cost.Section 4: Marginal Cost Results. The competitive price is within themarginal-cost range of every competitive generator and within the marginal-costrange of the market. If even one supplier has a supply curve that is continuous atthe market price, the market supply curve is continuous at that price and thecompetitive price is equal to the standard marginal cost which is well defined. Inany case, the competitive price is the price at which the supply and demand curvesintersect. Section 5: Working with Marginal Costs. This book assumes that supplycurves have extremely large but finite slopes rather than the infinite slopes fre-quently assumed. This is a more realistic assumption and has no practical conse-quences, but it has the simplifying property of making marginal cost well definedand the marginal cost of all operating competitive generators equal to the marketprice. Section 6: Scarcity Rent. Scarcity rent is revenue less variable cost and isneeded to cover startup and fixed costs. Economics refers to this as inframarginalrent, and has no separate definition of a scarcity rent. A folk-definition definesscarcity rent as actual revenue minus the maximum revenue that is collected justbefore the system runs completely out of capacity. Used with a stylized model, thisdefinition has some appeal, but when applied to real systems it is highly ambiguousand misleading.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.62 PART 1 Power Market FundamentalsFigure 1-6.1Adding individual supplycurves horizontally tofind the market supplycurve. If B is continuous,A +B is also.1-6.1 THE ROLE OF MARGINAL COSTMarginal cost plays a key role in the economic theory that proves a competitivemarket is efficient, but there are also two practical uses of marginal cost thatincrease its importance in a power market. First, many power markets rely on acentral day-ahead auction in which generators submit individual supply curves andthe system operator uses these to determine the market price. Because price shouldequal marginal cost in an efficient market, the auction rules should be informedby a coherent theory of marginal cost. Second, many power markets suffer frompotential market-power problems which cause the market price to diverge frommarginal cost. Market monitors need to understand this divergence.Although the competitive market price usually equals the marginal cost ofproduction, it is not determined by that alone. At times marginal cost is ambiguous,yet the competitive price is not. Then, marginal value (to customers) plays thedecisive role. The competitive price is determined by the intersection of the marketssupply and demand curves. Marginal cost determines only the supply curve.A supply curve can be thought of as answering the question, How much woulda generator produce if the market price were $P/MWh? As explained in Section1-5.3, price-taking suppliers adjust output until marginal cost equals the marketprice. As a consequence, if Q is the quantity supplied at a given price P, then Pmust equal the marginal cost. Thus a price-takers supply curve and marginal costcurve are the same.The markets supply curve, also called the aggregate supply curve, is foundby summing horizontally all of the individual generators supply curves. For a givenprice, the quantity supplied by each generator is read horizontally from eachindividual supply curve and these quantities are summed to find the market supply.This quantity is plotted at the given price, as shown in Figure 1-6.1.Notice that because one generator has a continuous supply curve (no verticalsection) the market has a continuous supply curve. Notice also that when bothgenerators are operating and have defined marginal costs, they have the samemarginal cost. Section 1-6.3 generalizes this by showing that every operatinggenerator either has a marginal cost equal to the market price or has a marginal-costrange that includes the market price.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-6 Marginal Cost in a Power Market 631-6.2 MARGINAL-COST FALLACIESDiscontinuous Supply CurvesIndividual supply curves are almost always drawn as hockey sticks. That is, theyare drawn with a slight upward slope (or as flat) until they reach the capacity limitof the generator and then they are drawn as perfectly vertical (see curve A, Figure1-6.1). Textbook supply curves usually have a slope that increases gradually (Seecurve B, Figure 1-6.1). Curves without a vertical segment are called continuous.Unfortunately, a generators supply curve, as typically drawn, takes an infiniteupward leap when it reaches full output (which is the most common output levelfor an operating generator). At this point, marginal cost is not smooth but jumpsfrom say $30/MWh to infinity with only an infinitesimal change in output. The smoothness of textbook supply curves plays a crucial role in keeping thetextbook definition of marginal cost simple, and this has led to mistakes andconfusion. Eliminating the confusion requires the introduction of a carefullyconstructed definition which applies to the discontinuous supply curves used inpower-market analysis. With this definition of marginal cost, all standard economicresults are found to apply to power markets. Once this is understood, the problem-atic supply curves can be analyzed correctly with a simple rule of thumb. Thisprovides guidance when setting the market price in a cost-base auction and whendetermining whether market power has been exercised. FallaciesTwo basic fallacies underlie a series of misconceptions surrounding competitivepricing and market power. These are (1) the Marginal-Cost Fallacy and (2) theAmbiguous-Price Fallacy. Both of these will be illustrated using Figure 1-6.2, whichshows a normal demand curve and a supply curve that is constant at $30/MWhup to an output of 10 GW, the capacity limit of all available generation.The Marginal-Cost Fallacy takes two forms. The simple form asserts thatmarginal cost at Q =10,000 MW is $30/MWh in Figure 1-6.2. The subtle formasserts that nothing can be said about the marginal cost at this output level. Someof the conclusions drawn from these assertions are as follows:1. The competitive price is $30/MWh, and the market should be designed tohold prices down to this level. 2. The competitive price is $30/MWh, and this is too low to cover fixed costs,so marginal-cost prices are inappropriate for power markets. 3. Scarcity rents are needed to raise prices above marginal-cost-based prices.4. Market power is necessary to raise prices to an appropriate level. 5. The competitive price cannot be determined.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.64 PART 1 Power Market FundamentalsFigure 1-6.2A normal marketequilibrium for anabnormal supply curve.The Marginal-Cost FallacyAll of these conclusions assume that there is some problem with standardeconomics caused by the supply curve coming to an abrupt end instead of turningup smoothly as it does in undergraduate texts. In fact, economic theory has nodifficulty with this example, and all of the above conclusions are false. Considera competitive market, with many suppliers and many customers, described by thecurves in Figure 1-6.2. What if the price in this market were $30/MWh? At thisprice, the demand curve shows an excess demand of about 4 GW. Some customerstrying to buy more power are willing to pay up to $70/MWh for another MW ofsupply. They will find a supplier and offer to pay considerably more than $30, andthe supplier will accept. This shows that the competitive price is above $30/MWh.The story will be repeated many times, with different values, until the market pricereaches $70/MWh. At that price every supplier will produce at full output, so thesupply will be 10 GW, and demand will be 10 GW. At any higher price demandwould fall short of supply, so the price would fall, and at any lower price, demandwould exceed supply, so the price would rise. There is nothing unusual about thisequilibrium; it is the classic story of how price clears a market by equating supplyand demand.

F FF Fallacy allacy allacy allacy 1-6.1 Marginal Cost Equals the Cost of the Last Unit ProducedMarginal cost equals the savings from producing less even when this is differentfrom the cost of producing more.(Subtle Version)Nothing can be said about marginal cost at the point where a supply curve endsor jumps from one level to another.But shouldnt price equal marginal cost? In this example, all that can be saidis that marginal cost is greater than $30/MWh. So there is no contradiction betweenprice and marginal cost, but they cannot be proven to be equal. The desire to pindown marginal cost precisely seems to arise from a belief that competitive suppliersshould set price equal to marginal cost and thereby determine the market price.But this logic is backwards. As explained in Section 1-5.3, suppliers set price toFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-6 Marginal Cost in a Power Market 65The Ambiguous-Price Fallacyclear the market and set quantity to bring marginal cost in line with price. In thisexample, the market-clearing forces of supply and demand determine price unam-biguously, and although marginal cost is ambiguous, it is greater than $30/MWhwhich is enough to determine supply unambiguously. Everything of practicalimportance is precisely determined.

F FF Fallacy allacy allacy allacy 1-6.2 When Marginal Cost Is Ambiguous, so Is the Competitive PriceCompetitive suppliers set price equal to marginal cost; thus when marginal costis hard to determine, the competitive price is hard to determine.Having analyzed the example, the preceding list of incorrect conclusions canbe restated in their.1. The competitive price is not $30/MWh, and the market design should nothold price to this level.2. The competitive price is high enough to contribute significantly to fixedcost recovery. 3. No mysterious scarcity rent need be added to the marginal cost of physicalproduction.4. Market power is not needed if the market is allowed to clear.5. The competitive price is $70/MWh.1-6.3 THE DEFINITION OF MARGINAL COSTThe above discussion is accurate but informal. Because of the controversy in thisarea, it is helpful to formalize the concepts used in analyzing supply curves withdiscontinuities or abrupt terminations.The MIT Dictionary of Modern Economics (1992) defines marginal cost as theextra cost of producing an extra unit of output. Paul Samuelson (1973, 451) definesmarginal cost more cautiously as the cost of producing one extra unit more (orless). The or less is important. The assumption behind this definition is thatproducing one more unit of output would cost exactly as much as producing oneless unit would save. This is true for the continuous marginal-cost curves oftextbook economics but not for the discontinuous curves used by power-marketanalysts. To discuss the marginal cost of a discontinuous supply curve, the definitionmust be extended to include the points of discontinuity where the cost to producean extra unit is distinctly greater than the savings from producing one less.Left- and Right-Hand Marginal CostsIn the example of Figure 1-6.2, the marginal cost of production goes from $30 onthe left of 10 GW to infinity on the right of 10 GW. This is a double complication.Not only does marginal cost change abruptly, it becomes infinite. The presentFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.66 PART 1 Power Market FundamentalsFigure 1-6.3Right- and left-handmarginal costs.definitions can be illustrated more clearly with a less pathological marginal-costcurve.Figure 1-6.3 shows the total cost curve and the marginal cost curve of a simplemarket. The discontinuity is the jump in marginal cost at the 10 GW output level.To the left of 10 GW the marginal cost is $20/MWh, while to the right it is$40/MWh. But what is the marginal cost precisely at 10 GW? It is undefined, but,as every textbook would confirm, the answer is not MC =$20/MWh.To formalize this definition, it is useful to consider the mathematics of the totalcost curve shown at the left of Figure 1-6.3. To the left of 10 GW, its derivative(slope) is $20/MWh, while to the right its slope is $40/MWh. But the mathematicaldefinition of a derivative breaks down at 10 GW, and since marginal cost is justthe derivative of total cost, the definition of marginal cost also breaks down at thispoint. Mathematics does define two very useful quantities at the 10-GW point, theleft-hand derivative (slope) and the right-hand derivative (Courant 1937, 199201).These are, of course, $20 and $40/MWh, respectively. Because marginal cost isjust the derivative, it is natural to define left-hand marginal cost (MCLH) as theleft-hand derivative, and right-hand marginal cost (MCRH) as the right-handderivative. Other points along the total cost curve also have left and right-handderivatives, and these are just equal to the normal derivative. Similarly, MCLH andMCRH are normally equal to each other and equal to standard marginal cost, MC.The marginal-cost range, MCR, is defined as the range of values between andincluding MCLH and MCRH. This definition is motivated by the idea that marginalcost cannot be pinned down at a point of discontinuity but can reasonably be saidto lie somewhere between the savings from producing one less and the cost ofproducing one more unit of output.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-6 Marginal Cost in a Power Market 671. Even those who best understand these concepts sometimes add to the confusion. Thus in the absenceof market power by any seller in the market, price may still exceed the marginal production costs of allfacilities producing output in the market at that time. (Borenstein 1999, 3) . . . the price of electricityhas to rise above its short-run marginal cost fromtime to time, or peaking capacity would never cover itsfixed costs. (Green 1998, 4).2. Part 3 discusses nonconvex costs, complexities of the production cost function that require deviationsfrommarginal cost. Essentially this means that startup costs and other short-run, avoidable costs must becovered by price.

Definitions Left-hand marginal cost (MCLH)The savings from producing one less unit of output.Right-hand marginal cost (MCRH)The cost of producing one more unit of output. When this is impossible, MCRHequals infinity.The marginal-cost range (MCR)The set of values between and including MCLH and MCRH.1-6.4 MARGINAL COST RESULTSRefining the Marginal-Cost Pricing ResultIn Figure 1-6.2, the MCLH at 10 GW is $30/MWh, but what is the MCRH? It istempting to say it is undefined, but again mathematics provides a more usefulanswer. The MCRH at 10 GW is infinite. This definition is both mathematicallysound and useful because it allows a simple rewriting of the standard economicresults concerning marginal costs.

Result 1-6.1 Competitive Suppliers Set Output so MCLH<

P <

MCRH

A competitive producer sets output to a level at which its marginal-cost range,MCR, contains the market price, P, whether or not that is the competitive price.First, a price-taking supplier will decrease output as long as P <MCLH becauseproducing one less unit will save MCLH and cost only P in lost revenues. Thus, thesavings is greater than the cost. Similarly, if MCRH<P, the supplier will increaseoutput. Thus whenever P lies outside the range between left- and right-handmarginal costs, the supplier will adjust output. When the range is below P, outputis increased, which raises the range and vice versa when MCR is above P. As aresult, the marginal-cost range will end up encompassing P. This means that in a competitive market, price will never exceed marginal cost;this would violate basic economics. Technically, P >MC can never be proven truein a competitive market.1 Competitive price will always be less than or equal toleft-hand marginal cost, and there is no need for it exceed this value for fixed costrecovery.2February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.68 PART 1 Power Market FundamentalsThe System-Marginal-Cost Pricing ResultFigure 1-6.4The smallest possiblechange in the supplycurve of Figure 1-6.2restores all normaleconomic properties.This result can be extended from a single producer to the whole market. TheMCRH of the market is the least cost of producing one more unit, so it is the mini-mum of the individual marginal-cost ranges. Similarly, the market MCLH is themaximum individual MCLH. In a competitive market, every supplier is a price takerand adjusts its output until P is within its marginal-cost range. Thus P is less thanor equal to every individual MCRH, so it is less than or equal to the MCRH of thesupplier with the lowest MCRH, which is the MCRH of the market. Similarly, P isgreater than or equal to the MCLH of the market.The range from the market MCLH to the market MCRH is contained within themarginal-cost ranges of each individual supplier. If even one supplier in the markethas MCLH=MCRH, the market will also have this property. In other words, if evenone supplier has a well defined-marginal cost at the market price, then the marketitself has a well-defined marginal cost.

Result 1-6.2 Competitive Price Equals System Marginal CostIn a competitive market, price is within the marginal-cost range of every generatorsupplying power. It is thus within the markets marginal-cost range. If even oneoperating supplier has a continuous marginal cost curve, the competitive priceactually equals marginal cost as defined by the aggregate supply curve.Finding the Competitive PriceFortunately the above results are needed only for untangling the current confusionsover marginal cost. They demonstrate, among other things, that price does notexceed marginal cost in a competitive power market.Fortunately, these results are not needed to find the competitive equilibrium,which is determined, as in any other market, by the intersection of the supply anddemand curves. This is most easily seen by smoothing out one of the problematicsupply curves very slightly.Standard economic theory applies once the vertical segments have been removedfrom the cost curves. This can be done with an arbitrarily small change in its shape.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-6 Marginal Cost in a Power Market 69As shown in Figure 1-6.4, giving the marginal cost curve a nearly, but not perfectly,vertical slope makes no noticeable difference to any economic result. And this ishow it should be. Economics should not and does not depend on splitting hairs.Notice that in the finitely-sloped model, price really does equal marginal cost atthe intersection of the two curves. The price and quantity dynamics of a marketwith the vertical supply curve will be essentially the same as those of the continuousmarket. In this example, at a price different from $70 and a quantity different from10 GW, the markets have essentially identical gaps between supply and demandand between price and marginal cost. So they adjust price and quantity in the sameway.

Result 1-6.3 Supply Intersects Demand at the Competitive PriceTo find the competitive price and the marginal cost, draw the supply and demandcurves, including the vertical parts of the supply, curve if any. The intersectionof supply and demand determines MC, P, and Q.This demonstrates that the standard method of finding the competitive equilib-rium works even when the marginal cost curves have infinite slopes. Of courseif the slope is infinite at the intersection of supply and demand, marginal cost willbe technically undefined. Yet pretending that the true marginal cost is determinedby this simple short cut will never give the wrong answer to any real-world question.1-6.5 WORKING WITH MARGINAL COSTSDiscussing left- and right-hand marginal costs and the marginal-cost range iscumbersome and unnecessary. If every vertical segment of a marginal cost curveis replaced with a nonvertical but extremely steep segment, the new curve will becontinuous and will not jump from one value to another. Such a change may ormay not improve its accuracy, but in either case it will make no detectable differ-ence to any economic prediction of consequence.This book will tacitly assume all supply curves and marginal cost curves thatare depicted as having vertical segments actually have extremely steep but finiteslopes. In other words, all marginal-cost curves are assumed to be continuous.Consequently, marginal cost is always a well-defined single value.For example, a supply curve that is constant at $30/MWh up to amaximum output of 500 MW can be replaced with one that is identicalup to 500 MW and then slopes upward linearly reaching a value of$30,000/MWh at an output of 500.001 MW. No measurement, howevercareful, could discern the difference. Yet this supply curve, beingcontinuous, has a well-defined value (marginal cost) at every level ofoutput.In fact most, if not all generators, have continuous marginal costcurves. Typically, they have an emergency operating range abovetheir nominal maximum output level and are willing to produce in thisregion if well paid or coerced. Most generators in PJ M include suchFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.70 PART 1 Power Market Fundamentals3. Personal communication fromJ oe Bowring, head of PJ Ms Market Monitoring Unit, J anuary 7, 2002.4. Samuelson (1973, 623) comes close to using the termwhen he says Competitively determined rentsare the results of a natural scarcity. His definition of such rents is the long-run analog of the short-rundefinition of scarcity rent given here.5. This is greater than short-run profit by the amount of startup costs and no-load costs which will beignored until Part 3.an emergency operating range in their bids and the total capacity available in thisrange is 1,900 MW out of a total installed capacity of about 60,000 MW.3 As longas there is one such generator in a market, the markets marginal cost curve iscontinuous. Real markets always have well-defined marginal costs and the competi-tive price equals that marginal cost. The difficulties resolved in this chapter onlymatter for the simplified diagrams used by power-market analysts.This book also will use the same simplified diagrams but without taking thevertical segments literally. Such supply curves will have constant marginal costsup to the nominal maximum output level, but above that marginal costs willincrease rapidly. If the supply curve is flat at $30 but the market price is $50, thegenerators marginal cost will be $50 and it will produce on the steeply slopedsegment. When referring to such a generator, it is both wrong and confusing to sayits marginal cost is $30 as is the custom. To avoid this confusion, the marginal costof a generators supply curve to the left of the maximum output level will betermed its variable cost. This is not entirely standard, but it is in keeping with theterms normal usage which refers to all costs that vary with the output level.1-6.6 SCARCITY RENTScarcity rent has no formal economic definition but many popularmeanings.4 Although several are useful, most do not lend themselvesto careful analysis. However, one essential economic concept comesclose to the popular meaning. Scarcity rent will be defined as revenueminus variable cost.5 Economics refers to scarcity rent as inframarginalrent.In the figure at the left, when demand is described by D1, bothgenerators are producing at full output, and load would be willing to payeither generator more than its variable cost of production if it wouldproduce more. In this sense they are both scarce and both earn scarcityrents.With demand reduced to D2, as shown in the lower half of the figure,generators of type G2 have excess capacity and are no longer scarce andearn no scarcity rent; their variable costs equal the market price. Genera-tors of type G1 are still scarce because load would be more than willingto pay their variable cost if they would produce more. If G2 had avariable cost of $1,000/MWh so that G1 were earning a rent of, say,$950/MWh because G1 could not satisfy the entire load, G1 wouldcommonly be seen as in scarce supply. The above definition coincideswith an important concept of economics and with the common meaning of scarcity.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-6 Marginal Cost in a Power Market 71Figure 1-6.5Folk-definition of scarcity rent.A Folk Definition of Scarcity RentSometimes, in the field of power system economics, scarcity rent is definedas actual revenue less the highest revenue earned before total generation becomesscarce. This might be called a folk definition. The notion is that until the systemruns out of capacity, price increases are due to increases in marginal cost, but afterthat point they are driven up by ever increasing scarcity. In an idealized model,this definition has some appeal.

Definition Scarcity RentRevenue minus variable operating cost (which do not include startup costs andno-load costs).Say there are only ten types of generators on the market, and call the one withthe highest variable cost the peaker. Next assume that there are no out-of-dategenerators with higher variable costs installed in the system. Finally assume thatno installed generator has an emergency operating range in which its marginalcosts increase dramatically as it increases its output beyond its normal rating. Withthese assumptions, peakers will earn enough to cover more than variable cost onlywhen the system runs out of capacity. In other words, peakers can cover their fixedcosts only from scarcity rents but not from any nonscarcity inframarginal rents.All other generators cover their fixed costs from a combination of scarcity andnonscarcity rents. The left half of Figure 1-6.5 illustrates this property of an ideal-ized supply curve.The folk definition has the advantage of allowing the following types of state-ments which seem designed to segregate scarcity conditions from the normaloperating conditions of the market.1. Scarcity rents pay capital costs of units that run infrequently.2. In the long-run competitive equilibrium, scarcity rents are just high enoughto cover the fixed costs of peakers.3. Scarcity rents are paid only infrequently.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.72 PART 1 Power Market FundamentalsThis appears to ratify the view that power markets are qualitatively different in theircost structure and consequently cannot be analyzed with the standard marginal-costapparatus. In the idealized model, these statements are true, although they give the impres-sion that scarcity rents are mainly or wholly associated with peakers. In fact, underthe folk definition, every type of generator receives the same amount of scarcityrent per MWh. In addition, the average scarcity rent in $/MWh does not equal thefixed cost of peakers but is greater by a factor of one over the duration of thepeakers use, something that is not easily determined.Two problems with this definition make it unworkable in a real market. First,there are likely to be old generators on the system with variable costs greater thanthe most expensive new generator that would be built (the peaker). In this casescarcity will not set in until the old generator is at full output. This will expand thenonscarcity rents and shrink the scarcity rents to the point where they no longercover the fixed costs of a peaker. Second, there will be some (probably many)generators with marginal cost curves that continue on up to some very high butill-defined value. This will reduce scarcity rents to some negligible and indetermin-able value. Proving scarcity rents exist requires proving price is above the pointwhere the supply curve becomes absolutely vertical; absolutes are notoriously hardto prove.Because of these shortcomings and the limited usefulness of the folk definition,this book will use only the definition given above that coincides with inframarginalrents, a term that has proven itself useful in economics. This is in keeping withthe chapters general view that generation cost functions present no new problemsof consequence and require only a minimal expansion of the definition of marginalcost and then only to deal with the stylized mathematics of discontinuous costfunctions.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-6 Marginal Cost in a Power Market 73A Marginal-Cost ExampleP Four suppliers can each produce 100 MW but no more.P Each supplier has constant marginal cost (MC) up to this limit.P Marginal costs and demand are as shown in the figure.If demand is given by D1,1. The competitive price is $60/MWh.2. Any higher price indicates market power.3. If the market is competitive, no supplier has MC <$60/MWh.If demand is given by D2 and the suppliers are price takers,1. The market price (P) will be $100/MWh.2. No generator will have a marginal cost of less than $100/MWh.3. No market power is exercised at this price.4. P is greater than the cost of the last unit produced ($60/MWh).In both cases the marginal-cost rule for competition isMCLH # P # MCRH *This is sufficient to determine the competitive market price and output.* MCLH is the savings fromproducing one unit less. MCRH is the cost of producingone unit more and is considered arbitrarily high, or infinite, if another unit cannotbe produced.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Thework I haveset beforemeis this . . . how to get rid of theevils of competition whileretainingits advantages.Alfred Marshall(1842-1924)Chapter 1-7Market StructurePOOR MARKET STRUCTURE POSES THE GREATEST THREAT TO THEHEALTH OF POWER MARKETS. Structure refers to properties of the marketclosely tied to technology and ownership. The classic structural measure is aconcentration index for the ownership of production capacity. The cost structureof an industry, another component of market structure, describes both the costsof generation and the costs of transmission.Most aspects of market structure are difficult to alter and some, such as the highfixed costs of coal-fired generation, are impossible. But power markets containsome unusual technology-based arrangements that can easily be altered or thatrequire administrative decisions regarding their operation. These arrangements arepart of the market structure and require design just as do the architectural compo-nents described in the next chapter.The notion of market structure developed as part of the structure-conduct-performance paradigm of industrial organization in the early 1950s. The presentdiscussion, however, is based on the structure-architecture-rules classification ofmarket-design problems presented by Chao and Wilson (1999a) and Wilson (1999).The present chapter extends their definition of structure, particularly in the directionof administered reliability policies.Chapter Summary 1-7: Market structure has a decisive impact on market powerand investment. The second demand-side flaw, the ability of users to take powerfrom the grid in real time without a contract (see Section 1-1.5), makes structuralintervention necessary. Regulators must trade-off price spikes against involuntaryload shedding, thereby largely determining the incentives for investment in genera-tion capacity.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-7 Market Structure 751. When considering the wholesale market, retail billing is part of structure. When considering the retailmarket it is simply a market outcome.Regulators will continue to control transmission investment either directly orthrough incentives. The strength of the transmission grid affects the marketscompetitiveness. Demand elasticity can be greatly enhanced by improved meteringand real-time billing, which can dramatically reduce market power and improvethe stability of generation investment. Long-term power contracts and supplyconcentration also play a key role in controlling market power.Because market structure is typically difficult to affect, it is usually ignoredby policy makers. The power market is unusual in this respect, partly because itis new, flawed, and utilizes the grid, a regulated shared asset. The present lack ofattention to market structure in the United States is producing unnecessarily highprice spikes, boom-bust investment cycle and problems with market power duringthe short-supply phase of the cycle. Part 2 discusses the structural design issuesmost crucial to the solution of these problems.Section 1: Reliability Requirements. The system operator buys energy andvarious grades of operating reserves to balance the system and to provide reliability.The number and type of submarkets used for this purpose are a matter of marketarchitecture, but the reserve requirements and price limits imposed administrativelyare matters of market structure.The structure of reliability requirements determine not only short-termreliability,but the height and frequency of price spikes and therefore long-run investment ingeneration and long-run reliability. These consequences of market structure areoften overlooked, so the design of the reliability structure is often inappropriate,sometimes with serious consequences.Section 2: Transmission. The transmission grid determines a significant partof the cost structure of the wholesale power industry. Investment in wires and thestructure of access charges both have significant impacts on long-distance tradeand thus on the markets competitiveness. This is an aspect of market structurewhich can and must be influenced by policy.Section 3: Effective Demand Elasticity. Demand appears to be inelasticbecause it is not given real-time price signals. It would be more elastic if customershad a reason to purchase and use the equipment necessary for responding to pricechanges. Policy can easily influence two key aspects of market structure, metersand billing, that would greatly increase effective demand elasticity.1 This wouldreduce the necessary investment in peak generating capacity, but more importantly,it would curb market power.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.76 PART 1 Power Market Fundamentals2. When considering the market for long-termcontracts, this is an outcome and not part of the marketsstructure. Section 4: Long-Term Contracts. The structure of the spot market includesthe extent of long-term obligations by suppliers.2 In new power markets, policycan influence this structural component. It can require vesting contracts for newlydivested generation and limit the amount of divestiture so obligations to loads atregulated prices are retained. Increasing the extent of long-termobligations increasesthe competitiveness of the spot market.Section 5: Supply Concentration. HHI, the classic structural index, measuresthe concentration of the ownership of productive capacity. While this aspect ofmarket structure significantly affects market power, it can be difficult to change,though it is easily influenced in new markets by divestiture requirements.1-7.1 RELIABILITY REQUIREMENTSThe Second Demand-Side Flaw. Electricity customers can take power in realtime without a contract and cause other customers to be blacked out, although inmost cases, they will suffer no disruption of their own. (See Section 1-1.5.) Rotatingblackouts are implemented without regard to contracts or consumption levels. Atsuch times, the system operator is faced with a difficult choice; it can pay evenmore for power or it can blackout more customers. The choice is easily made infavor of reliability when the price is within ten times the long-run average, but whenit increases to 100 times normal, the correct choice is less obvious. At some price,every system operator chooses to interrupt customers rather than pay the price.Operating Reserve Requirements. Deliberate interruptions of service are rareevents, but their possibility has an enormous impact on the market. To avoid them,power systems buy several kinds of operating reserves, generators that are paidto be ready to provide power at a moments notice. Together these reserves amountto approximately 10% of load at any given time.Normally the effect of operating reserves on market price is modest. Whenavailable capacity exceeds load by 10% or more, a competitive market will holdthe price of power down to approximately the variable cost of the most expensivegenerator producing power. In the normal operating range, this is under $100/MWh.In a year when system load never exceeds the normal range, prices are modest inspite of the administered operating reserve requirement. In fact prices are so lowthat generators cannot cover their fixed costs. If this situation were to continue yearafter year, no new generators would be built, and this would be the right outcome.Price Spikes and Investment. As consumption increases, supply becomestighter, and the system operator finds it impossible to maintain a 10% operatingreserve margin at all times. When reserves run short, the system operator offersto pay more either for power or reserves and this drives up the price of energy. Thisdynamic is the source of the high prices that induce investment. The heart of thisprocess is the administrative decision about how much to pay depending on howFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-7 Market Structure 773. The proposition that a price limit in the real-time market effectively caps the forward markets was welltested by the California Power Exchange.4. This assumes that the rules are at least modestly functional.low operating reserves are. This links concerns about reliability with the incentiveto invest. The high prices paid by the system operator to meet reliability requirementscontrol all high prices in the power market. Customers can choose between forwardpurchases and letting the system operator buy power for them in real time, and theychoose the cheaper alternative. This holds the price in all forward markets downto the price that the system operator charges for real-time purchases, and it chargesonly as much as it pays. So the price paid by the system operator sets a limit onthe price paid in all markets.3 During the intervals when its requirements foroperating reserves are not met, the system operators pricing policy controls theprice spikes and high forward prices that induce investment.Structure vs. Architecture of the Balancing Market. The balancing marketkeeps supply and demand in balance until the system operator is forced to balancethe system by shedding load. This market must be administered by the systemoperator, but it may include a sizable bilateral component. It may be integrated withthe markets for operating reserves, or these may be separate. These are questionsof market architecture. At a more detailed level, there are innumerable choicesconcerning market rules.The market rules and architecture do not determine the height and duration ofreal-time price spikes, nor how closely voltage and frequency will be maintained,nor the chance that the system will not recover from an unexpected generationfailure.4 These fundamentals are determined by the structure of the balancingmarket. The rules and architecture determine how efficiently trades are organized,who gets their transaction terminated when reliability is threatened, and how closelyprices approximate the competitive level.The structure of the balancing market is in part determined by the interconnec-tions reliability authority (NERC) and in part by local design. It is also influencedby the regional regulatory authority (FERC) when it caps real-time prices. Theaccuracy of balancing and short-term reliability are largely determined by thestructure of the balancing market. Less obviously, price spikes, generation invest-ment and long-term reliability are also largely determined by the balancing market.From this perspective, current balancing market structures appear haphazard andinappropriate. Part 2 examines these problems and presents methods for designinga better structure. 1-7.2 TRANSMISSIONMarket structure includes the arrangement and capacity of power lines. Insufficientcapacity can cause bottlenecks and local market power while additional capacitycan expand the size of the market and reduce market power. The effect of transmis-sion on market power makes transmission expansion more valuable in a competitivethan in a regulated market. February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.78 PART 1 Power Market Fundamentals5. Must-run generators are paid regulated prices, which are sometimes quite high, when they arerequired to run due to transmission constraints.While this structural component can only be changed slowly, it is one whosedesign cannot be ignored. Unless there is a reversal of the 100-year trend, new lineswill be needed for reliability and economy as demand for power continues to grow.These will be built either at the direction of market designers working for the systemoperator or by for-profit transcos whose incentives, determined by regulators,govern their choice of transmission upgrades. So far, this structural component has received the most attention, and the designissues have proven to be complex and contentious. Australia, New Zealand,Argentina, Alberta, California and Britain have all provided examples of transmis-sion design issues that have been resolved with only partial success. Albertas caseis particularly interesting because it has highlighted the trade-offs between transmis-sion and generator location. Albertas for-profit Transmission Administrator chosenot to upgrade Albertas major transmission path and instead offered long-termincentives to new generation investment in locations that would alleviate the needfor more transmission. This was quite successful, but two years later the TA stronglyfavored the now unnecessary upgrade in order to facilitate exports from northernAlberta to the United States.Albertas transmission issues did not involve the impact of transmission onmarket power, but in both Australia and California, this has been a prominentconcern. Due to their historic rivalry, Californias two largest investor-ownedutilities are connected by inefficiently small power lines (Path 15). As a conse-quence, these frequently inhibit trade, causing increased generation costs andincreased market power. Besides such major bottlenecks, there are dozens of smallerones causing infrequent but locally severe market power. Over half of the generatorsin California are regulated at times, supposedly because of these transmissionlimitations.5 While a must-run classification is sometimes only an excuse for aprofitable regulatory must-run contract, many cases reflect real transmissionconstraints.1-7.3 EFFECTIVE DEMAND ELASTICITYPerhaps the most dramatic structural problem of power markets is the almostcomplete lack of demand response to fluctuations in the wholesale price. It isconceptually dramatic because it sometimes prevents the intersection of the marketssupply and demand curves, a flaw so fundamental it is not addressed in any econom-ics text. Its consequences grab headlines when California suffers blackouts andNew York prices surge above $6,000/MWh. It is the flaw that makes market powera major issue in so many power markets that are otherwise well structured. Butwhat is puzzling is that the remedy is straightforward and would pay for itself. Thatsuch a cheaply fixed fundamental flaw has been consistently overlooked is duein part to confusion over the supposed costliness of real-time rates. But it is alsopart of the pattern of ignoring structural problems in favor of architectural problemsand disputes over market rules. February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-7 Market Structure 796. This demand-side flaw was largely responsible for Californias market power problems and blackouts.This fact is often ignored because the flaw, being structural, is considered akin to a law of nature and thusautomatically exempted fromblame.7. This result is based on the following real-time rates. Let Q(t) be the base profile that would becharged the flat monthly rate. A real-time customer that actually uses R(t) is charged at the flat rate times[the real-time cost of R(t) divided by the real-time cost of Q(t)].When the cost of delivered power is $1,000/MWh instead of the normal$35/MWh, most customers will save only $35 by consuming a megawatt less. Theydo not respond to the delivered cost of power because they receive no credit fortheir response. Their meters do not track their usage in real time. The problem isnot so much low demand elasticity as lack of pricing. In addition, because customersdo not face marginal-cost prices, most have developed little capacity to respond.This problem can be addressed either indirectly through architecture or directlyas a structural design problem. The indirect approach is to add competitive retailmarkets to the mix of wholesale markets in the hope that they will change thewholesale market structure by installing more real-time meters and implementingreal-time rates. The evidence so far is not encouraging. One direct approach wasinitiated in California in the spring of 2001 in response to dramatic market failures,many of which were greatly exacerbated by this demand-side flaw.6The direct approach requires installation of more real-time meters and implemen-tation of real-time retail rates. The former is trivial. California extended real-timemetering of load from 8 to 13 GW in just a few months at a cost of $25M, theamount of money one utility was losing per day at the height of the crisis. Real-timerates would be simple if customers were not risk averse, but they are, and so itrequires care to implement an appropriately hedged pricing scheme. California hasadopted a complex administrative approach to hedging that requires documentationof a customers past usage patterns and a series of continuing corrections wheneverplants and equipment are expanded or changed for reasons not related to energyconservation.To hedge a customers bill under real-time rates, the customers usage shouldbe divided into two parts, a base usage and deviations from the base. The basecan be defined in many ways, and this determines the complexity of the plan andthe properties of the hedge. By defining the base as the average of the customerclass, or in some other mechanical way, instead of relying on the past usage of eachcustomer, the plan can be greatly simplified. Also, the extent of hedging can bevaried. For instance the pricing plan can guarantee that customer bills will beimmune to monthly changes in the average real-time wholesale prices. Althoughthis prevents customers from reacting immediately to changes in the long-run pricelevel, they still feel the full effect of hourly price changes (scaled to remove thechange in the average monthly price).7The essential point is that effective demand elasticity is a crucial structuralparameter that is easily affected by policy, and there are many opportunities forclever market design. Typical values of the parameter are so unfavorable to marketstructure and improvement is so manageable that no power market should be startedwithout implementing a major real-time rate program.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.80 PART 1 Power Market Fundamentals8. See Borenstein, Bushnell, and Wolak (2000), the California Independent SystemOperator (2000),J oskow and Kahn (2001a and 2001b), and Wolak, Nordhaus and Shapiro (2000).9. The vesting contract should not specify which plants are providing the power, only that the new ownerof the plant will provide the power. This has the desired effect on market power without unnecessarilyrestricting plant operation. See Wolak (2000) for the effectiveness of vesting contracts.1-7.4 LONG-TERM CONTRACTSLong-termcontracts and regulatory obligations to serve load are an often overlookedaspect of market structure. These can greatly increase competitiveness in the spotmarket. A generator that has sold 90% of its power forward has only 1'10 theincentive to raise the price in the spot market as an identical generator that has soldnothing forward. If a utility sells half of its generating plants, it will become short of generation,need to buy power, and have an incentive to hold down the market price. But,without long-term contracts, the nonutility generators (NUGs) that bought theseplants will have a strong incentive to raise the price. Because the NUGs have moreability to raise the price than the utility has to hold it down, the net result can bea significant increase in market power. This happened in the California market.8To avoid this problem, it is both customary and advisable when plants aredivested to require that the purchasers sign vesting contracts to sell most of theoutput back to the utility for an extended period of time.9 This hedges the utility(preventing a California-style bankruptcy) and dramatically reduces the marketpower of the suppliers who bought the divested generation. The price of the long-term contract can be indexed to fuel costs and inflation but should not be indexedto the spot market wholesale price. Such vesting contracts were used extensivelyin Australia and have served to keep wholesale prices low under almost all marketconditions.Vesting contracts can dramatically improve market structure at the time ofdivestiture, but in the long run, the permanent market structure and design willdetermine the equilibrium level of long-term contracts. This is a topic of greatimportance that is in need of research.1-7.5 SUPPLY CONCENTRATIONSeveral indexes have been invented to measure supplier concentration; the bestknown is the Herfindahl-Hirschman Index (HHI). (See Chapters 4-3 and 4-5.)These indexes are of little use for predicting market power because concentrationis only one of several important determinants, but this problem with HHI does notreduce the importance of concentration.The two most effective methods of controlling concentration are divestiturerestrictions and limitations on mergers. Utilities are frequently required to limitthe amount of capacity sold to any single investor. For example, purchasers mightbe forbidden to own more than 5% of the total capacity inside a markets territory.In small markets, the purchasers of particularly large plants might need an exemp-tion from this requirement simply because a single plant exceeds the 5% limit.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-7 Market Structure 8110. Alberta, a relatively small market, has attempted to avoid the conflict between small concentrationratios and efficiency by selling twenty-year contracts for a plants control and output, while leaving theplants operation and ownership in the hands of the utilities. It remains to be seen how well this hasworked.Note that the stricter the limit, the less valuable the plants will be. Exercisingmarket power is more difficult for those with a smaller market share. Because alower limit on market share reduces the profitability of generators, it reduces theprice they will fetch when sold. Consequently, the utility required to divest willoppose any reduction in such a limit. It will argue that economies of scale or scoperequire a purchaser to own a large amount of capacity in order to operate a plantefficiently. These can be important effects, particularly when several plants arelocated on a single site, but disinterested expert opinions should be sought on theextent of such economies. Many suppliers own very little capacity in a market. Mosteconomies from multiple plant ownership can be achieved by owning plants indifferent markets.10February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. This chapter owes a great debt to Wilson (1999) and Chao and Wilson (1999a), though it is notintended as a summary of their views.Thewholeworld may belooked upon as a vast general market madeup of diversespecial marketswhere social wealth is bought and sold. Our task then is to discover thelaws to which thesepurchases and sales tend to conform automatically. To this end, weshall supposethat themarketis perfectly competitive, just as in puremechanics wesuppose, to start with, that machines areperfectly frictionless.Leon Walras Elements of PureEconomics1874Chapter 1-8Market ArchitectureA MARKETS ARCHITECTURE IS A MAP OF ITS COMPONENTSUBMARKETS. This map includes the type of each market and the linkagesbetween them.1 The submarkets of a power market include the wholesale spotmarket, wholesale forward markets, and markets for ancillary services. Markettype classifies markets as, for example, bilateral, private exchange, or pool.Linkages between submarkets may be implicit price relationships caused byarbitrage or explicit rules linking rights purchased in one market to activity inanother.Architecture should be specified before rules are written, but it is often necessaryto test the architecture during the design process, and this requires a rough specifica-tion of the rules. Architectural design must also consider the market structure inwhich it is embedded, which may inhibit the proper function of some designs.Market design should not be rigidly compartmentalized, yet it is useful to considerthe markets architecture apart from the details of the rules and the limitations ofmarket structure.Chapter Summary 1-8: A market design or analysis project concerns a collec-tion of submarkets which are collectively referred to as the entire market. (Bothwill often be referred to simply as markets.) Deciding which submarkets shouldbe created for a power market is the first step in architectural design. Section 1-8.1briefly discusses day-ahead and real-time energy markets and transmission-rightsmarkets as a prelude to Part 3 which examines these choices in more depth.Private submarkets range from disorganized to highly centralized, and each hasits advantages. There is no simple rule for choosing between types of submarketsFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-8 Market Architecture 83once one has been included in the design list. By bringing the entire market intofocus and specifying the markets architecture, the designer can take account oflinkages between markets and decide on the types of submarkets. The architecturalapproach to design helps with understanding interactions and relationships betweensubmarkets and thus with avoiding the proverbial Chinese menu approach.Linkages are the heart of market architecture, but the science of linkages is notwell developed. Timing, location, and arbitrage are the keys to most naturally arising(implicit) linkages, while explicit linkages are limited only by the imagination ofthe designer. Unfortunately many of these have unpleasant side effects. A carefulexamination of the markets architecture is the best antidote to inappropriatelydesigned linkages.Section 1: Listing the Submarkets. The architecture of the entire marketincludes the list of both designed and naturally occurring submarkets. Manycontroversies surround the questions of which particular submarkets to include.For example, a day-ahead centralized energy market may or may not be included,and some suggest that the only designed markets to include are those for transmis-sion rights and ancillary services.Besides the designed submarkets, others already exist or will arise naturally.If these play an important role in the functioning of the entire market, they are partof its architecture.Section 2: Market Types: Bilateral Through Pools. Bilateral markets canbe, in order of increasing centralization, search, bulletin-board, or brokered markets,while mediated markets can be dealer markets, exchanges, or pools. Public central-ized markets tend to have certain advantages over private markets that are decentral-ized: lower transaction costs, quicker transactions, greater transparency of price,and easier monitoring. Decentralized private markets are more flexible whilecentralized private markets are similar to their public counterparts.Energy exchanges accept only bids that, according to their bid-in values, at leastbreak even. Pools accept some apparently losing bids. Accepted bids that wouldotherwise lose money are compensated with a make-whole side payment. Ex-changes do not make side payments. Pools typically use much more complex bids,though exchanges can also use multipart bids.Section 3: Market Linkages. Implicit linkages are most often produced byarbitrage, the most important example being the arbitrage-induced equality betweena forward price for delivery at time T and the expected spot price at that time. Theselection and arrangement of submarkets can take advantage of implicit links aswhen ancillary-service markets are sequenced so that excess supply in one spillsFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.84 PART 1 Power Market Fundamentalsinto the next. Alternatively, multiproduct markets can be designed with explicitlinkages, sometimes increasing efficiency but also adding complexity.1-8.1 LISTING THE SUBMARKETSThe term market is used in many ways and has no strict definition. Tirole (1997)explains that it should not be so narrow as to encompass only a specific productproduced at a specific location, nor should it be the entire economy. He concludesthat there is no simple recipe. In practice, the market designer must choose adefinition to suit the problem at hand by relying on common sense rather thantheory.At least two categories of market are needed. First the designer must definethe scope of the design problem which will be termed the entire market. Powermarket in the present book refers to such a market. Depending on context this couldinclude only the wholesale market or the retail market as well. This choice demon-strates the need for a second market concept. An entire market typically includescomponents that are themselves markets. These will all be called submarkets. Thedistinction between an entire market and a submarket is relative, not absolute. Ina different context it could be useful to view the ancillary services market as anentire market with submarkets instead of as a submarket of the entire power market.An entire market may comprise many or few submarkets depending on its degreeof vertical integration or unbundling. In other words, the intermediate productsused to produce the final products of the entire market can be produced internallyby the producer that uses them or can be purchased in a submarket. The first stepin mapping an entire markets architecture is to decide on the list of submarkets.This is a key step in the design, requiring careful consideration, and it can be highlycontentious. Currently, there is no consensus, even within the most informed circles,as to the best collection of submarkets from which to construct a power market.J ust as for a market, there is no simple recipe for the definition of a submarket.If a day-ahead energy market contains two zones, then different suppliers will sellinto each zone and there will be two prices. Clearly there are two products: energydelivered to zone 1 and energy delivered to zone 2. Should these be considereddifferent submarkets? That may prove convenient, but when there are 500 locationswith different prices it will be necessary to count it as a single multiproductsubmarket. Conversely, PJMs day-ahead (DA) market sells energy and transmission rights.Although the prices of these are strongly linked, they are such different productsthey should be considered as supplied by two distinct but closely linked markets.Whether the transmission-rights market belongs on the list is distinct from thequestion of the energy market. For a given project, some submarkets need to be designed and some do not.The energy futures market at Palo Verde was not designed as part of the Californiarestructuring process though it is an important part of that power market. Generally,private markets will not be part of a design project of the type contemplated, though,when centralized, these markets are privately designed. Submarkets that are de-February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-8 Market Architecture 85signed as part of the public design process contemplated here are by definitionpublic markets and are almost always centralized. Submarkets that play a significantrole in an entire market should be included in the list of markets even if not designedas part of the current project because they are a vital part of the markets architec-ture. Linkages between designed and naturally occurring or pre-existing submarketsare crucial to the health of the entire market.A Public Day-Ahead Energy SubmarketThe question is not whether a DA energy market belongs on the list. If the systemoperator does not provide one, a private market will develop. But from the marketdesigners perspective, the question of whether the system operator will run a DAenergy market is crucial. For this reason the public and private DA energysubmarkets should be considered distinct. If a public DA market is added to thelist, there will still be the question, discussed in Section 1-8.2, of what type ofmarket it should be.If a centralized DA energy market is left off the list, a decentralized market mustcertainly be included because one will develop and play an important role in theentire market. Even with a centralized DA market, a private bilateral market is likelyto develop and should be included.Energy vs. Transmission SubmarketsPerhaps the most fundamental controversy concerning which submarkets belongin a power market concerns the question of whether the system operator shouldoperate an energy market or a transmission-rights market. One view holds that thesystem operator is only needed to operate the grid and sell rights to its use, but itshould minimize its role in the market and refrain from trading or pricing energy.A centralized transmission-rights market belongs on the list, but a centralized energymarket does not. The extreme version of this view would eliminate not only thecentralized DA energy market just discussed but also a centralized real-time (RT)energy market.The opposing view holds that such an architecture, plausible in a simplifiedtheoretical world, is wholly impractical. At least in real time, the system operatorneeds to buy and sell energy directly and needs to set different prices for energyprovided at different locations. A real-time locational energy market should be onthe list. The extreme version of this view holds that public DA and RT transmission-rights markets are not needed.Reasons for Including a SubmarketAn entire market typically consists of a set of closely related end-product marketsand the intermediate-product markets that feed into them. For a power market, theend product markets might be only a single wholesale electricity market in aparticular region. Wholesale markets include all forward, futures, and optionsmarkets. The difficult task is to decide which public markets should be created.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.86 PART 1 Power Market Fundamentals2. Motivations 1, 3, 4, and 5 are discussed in Chao and Wilson (1999a, 29).3. See the statement of the first welfare theoremin Mas-Collel et al. (1995, 308).While there are no clear-cut rules, several possible motivations should be consid-ered:1. Nondiscriminatory access.2. Completeness (trading of a product not otherwise traded).3. Reduced trading costs.4. A publically known price.5. Transparent operation.Nondiscriminatory access may be guaranteed by the governance structure ofa public market and is usually of most importance to small consumers and produc-ers.2 Completeness is most relevant in the case of public goods such as reliabilityservices. It may also apply to natural-monopoly goods and services such as the unit-commitment service. A public centralized market, such as an exchange, willtypically have much lower trading costs than a private decentralized market butnot necessarily lower than a private exchange.A publically known price serves two different purposes. First, it is a requiredassumption of the Efficient-Competition Result and is quite helpful to traders inmaking efficient trades.3 Second it can be used as a benchmark for other transac-tions, both regulated and private, such as settling financial futures. Transparentoperation is essential when market power is a potential problem and needs to bemonitored. There are also drawbacks to public markets, all of which seem related to thelack of proper incentives for regulators. A public market may offer products thatare not well designed or are too limited, or transactions costs may be higher thannecessary. These possibilities argue both for higher quality public institutions andfor the substitution of private ones.1-8.2 MARKET TYPES: BILATERAL THROUGH POOLSThere are two basic ways to arrange trades between buyers and sellers. They cantrade directly, one buyer and one seller making a bilateral trade, or suppliers cansell their product to an intermediary who sells it to end-use customers. Both bilateraland mediated markets come in several types with bilateral markets usually lessorganized but with some overlap in this regard.Entire markets often use a mixture of types. For example, the used car marketis a mixture of direct search, bulletin board, and dealer markets. The New YorkFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-8 Market Architecture 874. The terms direct search market, brokered market, dealer market, and auction market aredefined in Bodie et al. (1996, 24).Stock Exchange (NYSE) uses an auction, although when the market is thin, itbecomes a dealer market. The term pool has a special meaning with regard topower markets. For years, utilities in some regions have organized their productionin power pools, some of which used a centralized dispatch. In a deregulated market,a pool is an exchange in which the supply bids are complex, and the system operatorcarries out a complex calculation to select and pay the winners.Some markets work better as one type and some as another. In the heat of debate,those favoring bilateral markets often imply that exchanges are in some way likecentral planning, socialism, or even communism, but these analogies contributelittle. Often the right answer is for an entire market to utilize both approaches side-by-side. The long-term energy market utilizes a bilateral forward market that tradesindividualized forward contracts and centralized futures exchanges that tradestandardized futures contracts. The transaction cost of trading in the forward marketis greater but provides flexibility while trading in the futures market provides noflexibility in contract form but is inexpensive.Bilateral markets can be either direct search markets or brokered markets andcan be more or less centralized. If the market is brokered, as is the housing market,the brokers do not actually buy or sell in the market but are paid a commission forarranging a trade. Some forward energy markets, thanks to the Internet, are noworganized as bulletin-board markets which are just a partially centralized varietyof a direct-search market.With the exception of the bulletin-board approach, bilateral markets need littledesign. They require an enforcement mechanism for complex contracts, but thisis provided by the pre-existing legal framework.Bilateral Markets, Dealers, Exchanges, and AuctionsIn bilateral markets buyers and sellers trade directly, although this is typicallyfacilitated by a broker. Such markets are extremely flexible as the trading partiescan specify any contract terms they desire, but this flexibility comes at a price.Negotiating and writing contracts is expensive. Assessing the credit worthinessof ones counter party is also expensive and risky. For these reasons there is a greatadvantage to moving toward more standardized and centralized trading when thisis made possible by the volume of trade.A dealer market is the most rudimentary type of mediated market.4 Unlike abroker, a dealer trades for his own account, and usually maintains an inventory.He buys the product and holds it before reselling. There is no brokerage fee, butat any point in time the dealer buys for a price that is lower than the price he sellsfor. This difference is called the spread.An exchange provides security for traders by acting as the counter party to alltrades, eliminating traders concerns over creditworthiness. Exchanges utilizeauctions and are sometimes called auction markets; the NYSE is an example. AsBodie et al. (1996, 24) point out, An advantage of auction markets over dealermarkets is that one need not search to find the best price for a good. Because anFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.88 PART 1 Power Market Fundamentalsexchange interposes itself between buyers and sellers, the two halves of the marketcan operate independently, although they are linked by what is called a doubleauction. (Auctions are a traditional method of implementing a competitive marketand are discussed in Chapter 1-9.)An exchange can have a number of advantages over a bilateral market. It canreduce trading costs, increase competition, and produce a publically observableprice. Depending on design and circumstances, it can also facilitate collusion andgenerally provides less flexibility than a bilateral market. Power marketers oftenfavor bilateral markets because without an exchange there is more room to earncommissions as brokers and to appropriate the spread when they act as dealers.Because exchanges are inflexible, they can operate much faster than bilateralmarkets. Stock exchanges routinely execute trades in under five minutes whilebilateral markets take hours to weeks. In power markets, speed is crucial. Catastro-phes can happen in seconds and system operators often need to exercise minute-by-minute control. Because of their speed, exchanges can operate much nearer to realtime than can bilateral markets. This makes them the obvious choice for the real-time market. Weeks in advance, bilateral markets and dealer markets may play alarger role than exchanges. In between, there is much room for disagreement overwhich is better. Exchanges vs. PoolsIf there is to be a public day-ahead market, should it be a pool or an exchange?PJ M, NYISO, and ISO-NE all adopted pools, but CA ISO adopted a combinationof public exchange (the Power Exchange) and private exchanges and dealers (theother scheduling coordinators). Although the California market has performeddisastrously, this probably has little to do with its architecture and everything todo with its structure. No conclusion regarding exchanges can be drawn from thisevidence. Californias Power Exchange was an exchange because it did not use the make-whole side-payments which characterize a pool. As is typical of exchanges, it usedsimple bids. These expressed only an energy quantity and price which meantgenerators could not take account of their startup costs and no-load costs directlywithin the bid format. Consequently, they had to manipulate or game their bidsin some way to avoid a loss. Chao and Wilson (1999, 48) discuss such a circum-stance as follows:Gaming strategies are inherent in any design that requires trad-ers to manipulate their bids in order to take account of factorsthat the bid format does not allow them to express directly.In order to avoid this problem, more complex bids, perhaps two or three part bids,are needed. Alternatively a pool could be used. Pools are defined by the existence of side payments. Generators bid theirmarginal cost and certain other costs and limitation into the pool which computesa price and a set of accepted bids. Some accepted bids are found to lose moneybecause the pool price is not enough higher than their marginal cost to cover theirFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-8 Market Architecture 89other bid-in costs. The pool makes up for this be granting accepted bidders, thatwould otherwise lose money, a side payment that makes themwhole. Because someapparently losing bids are accepted, losing bidders have no way to verify whethertheir bid was correctly rejected. Typically pools utilize very complex bids whichattempt to comprise a complete economic description of the generation process,but this is not necessary. A pool could be designed with two-part bids.Although the principle of designing bid formats so that they do not requiremanipulation is a useful one, it need not be carried to extremes. Another principlestates that, in a competitive market, competitive forces will induce bidders torepresent true costs as accurately as possible within the bid framework. Thus inthe Power Exchange, bidders included in their bids expected startup and no-loadcosts as well as their marginal costs. Chapter 3-9 shows that even in an exchangewith one-part bids, where considerable manipulation is necessary, a competitivemarket will do a remarkably efficient job of dispatching generation. The gamingexhibited in a competitive market with an inappropriate bid format is largelybeneficial and should probably be described by another name.1-8.3 MARKET LINKAGESMarket linkages, aside from arbitrage, have no standard classification or nomencla-ture. Nonetheless they are tremendously important to the functioning of the entiremarket. Linkages can be either explicit or implicit. For instance, the requirementto purchase a transmission right, in order to inject and withdraw power, is an explicitlinkage between the market for transmission rights and the bilateral market forwholesale energy. An implicit linkage causes the price in a forward energy marketto approximate the expected price in the spot market during the forwards deliveryperiod. There is no rule that enforces this relationship, only the discipline ofarbitrage. Implicit links are not designed, but they are an important part of thearchitecture and must be reckoned with.Sometimes when explicit linkages are needed, it indicates that two marketsshould be merged into a multiproduct market. Implicit linkages occur naturally andare usually helpful; explicit linkages are helpful when they reflect real costs. Theyare frequently harmful when they reflect a preconceived notion of how the marketshould operate. Because power markets are geographically distributed, many of their submarketsare multiproduct markets and contain vast arrays of internal linkages. When thetransmission system is congested (or if losses are charged for, as they should be)energy at location A is technically a different product from energy at location B.This is not just an academic definition. A completely unregulated bilateral marketwill price energy differently at the two locations. Consequently, an energy marketis a multiproduct market with internal linkages between the products.J ust as there are spacial linkages, there are also temporal linkages. Marketarchitecture establishes the temporal order of markets, and this order causes implicitlinkages to develop between the markets. Both temporal and spacial linkagespervade the architecture of power markets.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.90 PART 1 Power Market FundamentalsThe Arbitrage Linkage of Forward to Spot PricesIn a well-arbitraged market the forward price for delivery at time T will equal theexpected spot price at time T. Because the market designer will find this commonlinkage extremely useful in understanding and predicting the behavior of entiremarkets, it is explained in some detail here.There are two types of arbitrage (Tirole 1997, 134). The first, and morecommonly recognized type, involves the transfer of a commodity froma high-pricedlocation to a low-priced location. The relevant type for this analysis involves thetransfer of demand from a high-priced product to a low-priced product. In thepresent case, customers can transfer their demand between forward purchases andspot purchases.Say a customer knows it will need a certain quantity of power at a future timeT. The customer can either buy an energy future now, at known price FT, to bedelivered at time T, or can wait and buy the power in the spot market at an as yetunknown price PT. Which is preferable? Payment on the future can be largelypostponed until delivery, so interest has a negligible effect. Generally a known priceis preferred to an unknown price, but the main effect is that FT will be preferredif PT is expected to be higher and vice versa. If E(PT) is the currently expected spotprice at time T, this can be summarized asFT<E(PT) causes futures to be preferred.FT>E(PT) causes spot purchases to be preferred.The result is that whenever FT is lower, demand for futures will increase and FTwill increase, while, if FT is higher, demand for futures will decrease, with the resultthat FT=E(PT).

Result 1-8.1 The Forward Price Is the Expected Future Spot PriceThe price of a future or forward specified for delivery at time T is approximatelyequal to the expected spot price at time T.This relationship is not exact. Both buyers and sellers tend to prefer the certaintyof knowing the futures price. If the buyers preference is stronger, FT may be greaterthan E(PT), and vice versa. These preferences will depend somewhat on the possibil-ities for diversifying the risks involved, but altogether these effects are too subtleand too unpredictable to be of interest to the power-market designer. For practicaldesign purposes, FT can be expected to equal E(PT).One immediate consequence is that if the real-time (spot) price is capped at$500, then the day-ahead price will not rise above $500. Of course if there arepenalties for trading in the spot market, these must be taken into account. This effectwas well documented in California, and it provides a mechanism for cappingmarkets that are not accessible to the system operator.Besides being a valuable tool for understanding the implications of systemarchitecture, this result can provide practical insight. Seeing current high spot marketprices and low future prices, i.e., FT<P0, many concluded that it was nearly alwaysFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-8 Market Architecture 915. This is explained in 3-1.3 and can be proven fromthat facts that in general PAB= ! !PBA and. PAB+PBC=PACmuch cheaper to buy forwards than to wait for the inevitable high spot price. Incontradiction of Result 1-8.1, they concluded that FT<E(PT), and probably muchless. This was one of two factors which led to Californias huge purchases offorwards in the spring of 2001. It now appears that purchasing all of Californiaspower requirements for 2004 from an extremely thin market during a powershortage, was not a sure bet. Pre-announcing a determination to buy no matter whatand using inexperienced traders compounded the problem. Most likely, Californiadid manage to create a temporary exception to the forward arbitrage linkage,FT=E(PT), but in the opposite direction from what motivated the purchases: FTwas probably much greater in California during the spring of 2001 than a rationalexpectation of future spot prices.Locational Price LinkagesConsider what happens if transmission rights are auctioned independently, as theyoften are. Suppose the right from A to B and from B to C and from A to C are allbid for separately, and the system operator sells them at the lowest set of pricesthat clears the market, given feasibility constraints on the rights. This would givethree prices, PAB, PBC, and PCA, but if the market is working efficiently, these priceswill be tightly linked and in particular will sum to zero. Arbitrage is also key tothis result, but the point is not the result itself but the fact that spacial linkages ofenergy prices are strong and important.5 This is just one of a number of such results.Cascading MarketsGenerators can provide energy or they can provide reserves, an option to buy energywhen more is needed. Various qualities of reserves are graded by the quicknessand sureness of their response. This classification provides an unambiguousordering by value with the best quality of reserve always preferred to the secondbest, and so on. Suppose there are three such products called R1 (best), R2, andR3, and the system operator requires a certain amount of each.If no linkage is made between the markets for R1, R2, and R3, they will takeplace simultaneously but separately. In this case any excess capacity in one marketcannot flow into the others to help lower the price in those markets, so the marketsshould be linked, at least by conducting them in sequence. If the R3 market wereconducted first, any excess of R2 might not be bid into the R3 market because itwould not yet be known that it was in excess. To achieve a cascade, the marketsshould be cleared starting with the highest quality. Any surplus R1 reserves couldbid into the R2 market and so on. This increases the efficiency of the marketsrelative to the absence of a cascade or one set up in reverse. Even with a forwardcascade these markets will not performoptimally. If there is a shortage in the marketfor R3 and in total, but not for the first two markets, the price in the R3 market couldexceed the other two prices. In this case high-quality reserve units would hold outfor a chance at the third market, which could result in an inefficient use of reserves.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.92 PART 1 Power Market FundamentalsEfficiency can be increased by collapsing the three into a single multiproductmarket with strong internal linkages. Such an arrangement will be simpler for thesuppliers but more complex for the system operator. The reserve market can alsobe integrated with the energy market. Every new level of integration brings newcomplexity to the market clearing mechanism and reduces its transparency, butit has the potential to increase efficiency. Making the proper trade-off betweenefficiency and internal complexity, with its attendant opportunities for design errorand gaming, is a controversial and unresolved issue.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. One of several design flaws that produced this outcome was prohibiting the California ISO fromsubstituting a cheaper better product for a more expensive poorer product (Wolak, 1999). Also see Brien(1999).Genius is oneper cent inspiration, ninety-nineper cent perspiration.Thomas Edisonc. 1903If Edison had a needleto find in a haystack hewould proceed . . . to examinestraw after straw.A littletheory and calculation would havesaved him ninety percent of his labor.Nikola TeslaNew York Times1931Chapter 1-9Designing and Testing Market RulesUNTESTED MARKET DESIGNS CAUSE REAL-WORLD MARKET FAIL-URES. Suppliers are quick to take advantage of design flaws, especially those thatpay $9,999/MWh for a product that is worth less than $5/MWh.1 Currently, manyif not most, market designs are implemented without any explicit testing.Although the most serious market flaws typically arise fromstructural problems,while architectural problems rank second in importance, problems with rules arethe most numerous and their cost can be impressive. The design of rules is moreart than science, but economics offers two guiding principles: mimic the outcomeof a classically competitive market, and design markets so competitors find itprofitable to bid honestly. Simplicity is another virtue well worth pursuing butnotoriously difficult to define.Chapter Summary 1-9: In a pay-as-bid auction, a coal plant bidding its variablecost of $12/MWh would be paid $12/MWh, while in a single-price auction it wouldbe paid the system marginal cost which might be $100/MWh. In this case manywould object to paying the $100 competitive price to the inexpensive coal plantand seek to improve on the competitive model. Pay-as-bid is one suggestion. Theresult is gaming and, probably, a very modest decrease in price and a modestdecrease in efficiency. Ironically, if pay-as-bid succeeded as its advocates hope,it would put an end to investment in baseload and midload plants. In the long runthis would dramatically raise the cost of power. The pay-as-bid fallacy illustratesthe topics of the first three sections: the danger in attempting to subvert competition,the benefits of incentive compatible design, and the relevance of auction theory.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.94 PART 1 Power Market FundamentalsThat testing is the key to successful design is well understood by engineers untilthey design markets instead of equipment. It is not well understood by policy makersor economists, and the results are predictable. Rigorous testing, though worthwhile,is expensive so a simple bottom-line test should always be conducted first. Thisonly requires building the simplest relevant model computing the cheapest possibleproduction costs, and then computing the costs under the proposed design. If theseare much different, reject the design. This test cannot prove a design will work,but it can save the cost of a rigorous test or a real-world failure. Section 1: Design for Competitive Prices. Competitive prices sometimesinclude a scarcity rent much greater than needed to cover the concurrent fixed costpayment. Frequently this inspires attempts, such as FERCs advocacy of pay-as-bidauctions, to redesign the market to pay a price below the competitive level. If sucha scheme were to succeed, it would cause reduced and distorted investment.Fortunately most such schemes are largely subverted by market forces.Section 2: Design to Prevent Gaming. Rules that induce truth telling arecalled incentive compatible and often provide good market designs. Some biddingrules force suppliers to submit bids that do not reflect their true costs; such rulesinduce gaming. The pay-as-bid auction design is an example. Gaming usually causesinefficiency, the importance of which needs to be evaluated on a case-by-case basis.Section 3: Auctions. Exchanges and pools use auctions to determine market-clearing prices. The four main auction types all produce the same revenue whenbidders are buying for their own use or selling their own product. There is a slightefficiency advantage for a second-price auction which is incentive compatible.Recent work in auction theory shows that these results do not generalize to themulti-unit auctions with elastic and uncertain demand characteristic of powermarkets. In this setting, results are ambiguous, but pay-as-bid auctions tend to inhibitmarket power, sometimes at the cost of reducing welfare.Section 4: Testing Market Rules. Every market design should undergo atleast minimal testing before use. A minimal bottom-line test consists of threesteps: (1) model the market with and without the design in enough detail to computethe designs impact on production costs, (2) find the minimum possible cost ofdelivered power, and (3) find the cost of delivered power when the market operatesunder the proposed rules. If the design raises costs significantly, it fails the test.Such a test cannot prove that the design will work well in the real world, but it oftenshows it will fail under even ideal conditions, a useful, if disappointing, result.Section 5: Technical SupplementExample of a Bottom-Line Test.A proposed charge for transmission access is tested and found to induce generationinvestment in a pattern that increases the total cost of delivered energy. Since theFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-9 Designing and Testing Market Rules 952. The Blue Ribbon Panel that examined this scheme for Californias Power Exchange concluded: Insum, our response is that the expectation behind the proposal to shift fromuniformto as-bid pricingthatit would provide purchasers of electric power substantial relief fromthe soaring prices of the electricpower, such as they have recently experiencedis simply mistaken. . . . In our view it would doconsumers more harmthan good." (Kahn et al., 2001, 17)3. Fromp. 4 of his concurrence with FERC (2000b).proposed design fails to perform under even the simplest network conditions, itcould have been rejected without expensive testing.1-9.1 DESIGN FOR COMPETITIVE PRICESMarkets should be designed to produce competitive prices, but especially in powermarkets, competitive prices sometimes appear disconcertingly high. While mostdesigners remain loyal to the ideal of competitive prices, many decide to redefinethem to be lower at times, and some decide that they are just not right. Recently FERC proposed a pay-as-bid auction design in the hopes of holdingprices below their competitive level.2 Several early proposals for the Californiamarket also had this intent. Even the PJ M market contains elements of this flaw.These initiatives reflect a basic misunderstanding of the role of scarcity rent(defined in Section 1-6.6).Scarcity RentIf a competitive generator sells 10,000 MWh for $500,000 and its variable operatingcosts are $100,000, then its scarcity rent is $400,000 which is not an unlikelyoutcome for a low-variable-cost coal plant when the market price is set by themarginal cost of a high cost gas turbine. Scarcity rents are necessary for suppliersto cover their fixed costs, which, as explained in Chapter 1-3, can be thought ofas a constant flow of cost equivalent to the cost of renting the power plant. Duringthe period in which the plant produced its 10,000 MWh, its fixed costs might havebeen $200,000. In this case the scarcity rent was twice what was needed to coverfixed costs during that period of operation. Such discrepancies are common, andthey convince many that competitive prices are often too high.

F FF Fallacy allacy allacy allacy 1-9.1 Scarcity Rents Are UnfairIf the price paid to generators always equals system marginal cost, generators withlower variable costs will be paid too much.This conclusion ignores the fact that in power markets, scarcity rents fluctuatedramatically. If they are to equal fixed costs on average, they must be highersometimes and lower other times. Typically they are lower most of the time butare occasionally much higher. Ignoring this leads to a fallacy which states thatpaying a low-variable-cost plant the marginal cost of an expensive plant is unfair.This was succinctly expressed by former FERC Chairman Curt Hbert.3

February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.96 PART 1 Power Market FundamentalsIf the market clearing price for the final increment of neededcapacity is, say, $100 MWh, why should a supplier who bid alower figure receive the same value as that afforded to the sup-plier of [the] higher-priced increment?There are two answers to this question. First, as explained below, if low bidderswere paid less, they would raise their bids. The Blue Ribbon Panel (Kahn, 2001),which analyzed FERCs pay-as-bid proposal for the California Power Exchange,focused entirely on this first answer. It explained what would have gone wronghad the proposal been implemented and it used auction theory for its analysis.The second answer and the root of the problem lies in the desire to hold pricesdown to their short-run limit. Notice that the concern is with a supplier who bida lower figure. Suppliers that bid low are lower-variable-cost, baseload suppliers,and they bid low in order to guarantee they will run. The chairmans question waswhy, with their low variable cost, they should be paid as much as the high-pricedsupplier. The answer is they have higher fixed costs and need more scarcity rentto cover them.Many schemes have been proposed to hold prices down to variable cost, andgiven sufficient regulatory authority they can be effective. Consequently it isimportant to understand that reducing price in the short run will increase it in thelong run. This is not true if prices remain at or above the competitive level, butthe competitive price pays higher and lower cost producers exactly the same whenthey both are needed at the same time. FERCs scheme was intended to holdbaseload prices well below the competitive level. The Efficient-Competition Resultstates that competitive price will, over the long run, induce the right investmentin both baseload plants and peakers. If regulators reduce the prices paid to baseloadplants, in the short run they can get away with it, but in the long run, investors willsee that baseload plants cannot cover their fixed costs and will build no more.How the Market Fights BackMarkets have ways of subverting the best-laid plans of regulators. Sometimes thiscauses problems, but in this case, it would prevent most of the damage that FERCsscheme would cause if it worked as intended. The plan was to capture the rent ofbaseload plants and thereby reduce prices. The method was to pay low bidders theirbid, and as Kahn et al. (2001, 5) explain:The critical assumption is, of course, that after the market rulesare changed, generators will bid just as they had before. The oneabsolute certainty, however, is that they will not.Markets are composed of clever, highly motivated players who spend a great dealof time and effort discovering the most profitable way to respond to changes inrules. The most fundamental mistake a market designer can make is to treat a marketas if it were a machine that does not change behavior when the rules change.Knowing that bids will change is easy; finding the new outcome of changedrules and changed behavior is more difficult. One approach is to take a close lookFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-9 Designing and Testing Market Rules 974. My preference is that sellers in California be paid what they bid, regardless of what that bid is, ratherthan the market-clearing price. Fromp. 4 of his concurrence with FERC (2000b).5. Another possibility is to match buyers and sellers by price so the $50 supplier sells to the $50 buyer,and so on. Applying the concept of total surplus fromSection 1-5.2 demonstrates that this yields no totalsurplus, while using a market-clearing price gives a total surplus of $20.at why the New York Stock Exchange does not follow Chairman Hberts prefer-ence that sellers ... be paid what they bid ... rather than the market-clearing price.4Why the NYSE Pays the Market-Clearing PriceEach stock on the NYSE accumulates bids and offers over night, and as the marketopens, these are traded at a single market-clearing price. Say there are three bidsto sell 100 shares each at $50, $60, and $70 per share and three bids to buy at $50,$60, and $70 per share. In this case, the Exchange will set a market-clearing priceof $60, and the two offers to sell for this much or less will be traded with the twobids to buy at this much or more. All will receive or pay the market-clearing priceof $60.If the NYSE followed FERCs scheme for running the California market, theopening of the stock market would work like this: The NYSE would accept thetwo bids from those selling stock (the supply or generator bids) at $50 and $60 andpay these two their bid price. They would then compute the average cost to be$55/share and sell the shares at that price to the buyers who bid $60 and $70/share.Instead of a single market-clearing price, the market would have one price for eachsupplier and a different but single price for all buyers.5The suppliers would then argue that the NYSE should have done just theopposite. They should have averaged the two buyers bids of $60 and $70 and paidboth suppliers $65 for their stock. They have a point. Why should sellers who bidlow receive only their bid price while buyers who bid high are not required to paytheir bid price. Are stock buyers more worthy than stock sellers?There is a more fundamental problem; traders will not sit idly by. The $50supplier would realize that a $60 bid would have been more profitable and the nextday bid $60. Then the FERCs scheme would produce the same result as theNYSEs market-clearing auction. If bidding low is rewarded with a low payment,while bidding the market clearing price is rewarded with the higher market-clearingprice, previously low bidders will become high bidders.

Result 1-9.1 Changing the Markets Rules Changes Behavior Auction Rules and Competitive PricesPredicting the effect of rules and rule changes is a difficult matter which is whySection 1-9.4 prescribes testing for all proposed rules. Many of the important rulesin power markets, including those just discussed, are auction rules and are thesubject of auction theory, an important and rapidly developing branch of economics.A principle goal of auction theory is the design of auctions that produce competitiveprices, and while much progress has been made, much remains unknown.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.98 PART 1 Power Market FundamentalsWhen considering auction rules, two categories of problems should be distin-guished: designing for a market with a competitive structure or designing for amarket with a monopolistic structure. A competitive structure implies the biddersare small relative to the size of the market, where small must be defined relativeto the markets demand elasticity. If bidders are large or demand inelastic, thestructure is monopolistic. Within a competitive structure, it is reasonable to askthat the auction rules produce competitive prices. In a monopolistic structure, aboutthe best that can be hoped for are auction rules that reduce the exercise of marketpower relative to alternative rules.When considering FERCs proposed pay-as-bid rule change, three questionsshould be asked:1. If the rule change worked as intended, would market prices be nearer thecompetitive level?2. In a competitive market structure, would the rule change bring market pricesnearer to the competitive level?3. In a monopolistic market structure, would the rule change bring marketprices nearer to the competitive level?The first question is about intentions, the second and third are about how the rulewould actually work. The answers to these three questions are: (1) No, baseloadprices would be reduced far below the competitive level. (2) No, prices would suffera mild increase in randomness and baseload prices would be reduces slightly belowthe short-run competitive level. (3) Quite possibly, but this might come with areduction in welfare. These results are discussed further in Section 1-9.3.1-9.2 DESIGN TO PREVENT GAMINGMarkets often require participants to state a price at which they would either buyor sell. The market then selects the buyers who name high prices and the sellerswho name low prices. This occurs in private bilateral markets and in public ex-changes. If the buyers who bid high have the highest values for the goods beingpurchased, and if the sellers who bid low have the lowest costs of production, thentheir trades will be efficient. All those who can produce for less than the marketprice will trade with all those with values above the market price.One way to arrange efficient trading is for all the traders to bid prices that areequal to their true costs and values. If all bidders tell the truth, the outcome isefficient. This is not the only way to get the efficient outcome, but it is the mostobvious. An economic theorem states that for a very broad class of markets, if anymarket mechanism can be designed to give the efficient outcome, then there mustbe one that works by inducing traders to tell the truth.Economists call a market mechanism that induces truth-telling an incentive-compatible mechanism. It not only makes the market efficient but also tends tobe easier to discover and simpler to implement. For these reasons economists lookfor incentive-compatible designs, but sometimes they are too complex or politicallyFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-9 Designing and Testing Market Rules 996. See Klemperer (1999; 2000a; 2000b) for surveys of auction theory and literature. The first is the mostaccessible.unpopular. In this case a less efficient design will usually need to be adopted, butit is generally useful to look for the efficient design first.

Result 1-9.2 Design Market Mechanisms to Induce Truth Telling If there is a market design that leads to an efficient outcome, then there is a designthat induces traders to tell the truth and produces that outcome. Such a design iscalled incentive compatible.The pay-as-bid auction discussed in the previous section is not incentivecompatible for it induces misrepresentation of variable cost. This is also calledgaming. As a consequence there will necessarily be some inefficiency unlessthe market price is always perfectly predictable. The single-price auctions of mostelectricity markets are nearly incentive compatible. Suppliers almost tell the truthwhen they are competitive (most of the time) but distort their bids when they havemarket power.1-9.3 AUCTIONSIn the last forty years, economics has developed an extensive theory of auctions.Perhaps because auctioning electricity is a rather new idea, some have suspectedthat auctions are an invention of theoretical economics. In fact, the Babyloniansused them in 500 BC, and Buddhists employed them in the seventh century.Sothebys was established in 1744, some time before Adam Smith gave economicsits start.6William Vickrey, who won the 1996 Nobel Prize in economics largely forhis work on auctions, classified one-sided auctions into four types.1. English: Buyers start bidding at a low price. The highest bidder wins andpays the last price bid.2. Vickrey (second-price): Buyers submit sealed bids, and the winner paysthe price of the highest losing bid. This is also confusingly called a Dutchauction.3. Dutch: The auctioneer starts very high and calls out progressively lowerprices. The first buyer to accept the price wins and pays that price.4. Sealed-Bid (first-price): Buyers submit sealed bids, and the winner paysthe price that is bid.These four types of auction can all be used in reverse to buy a product insteadof sell it. For example, in a reversed English auction, sellers can call out progres-sively lower prices until there are no more bids. The lowest bid wins, and the sellersells at that price. Consequently everything said about auctions to sell, holds forauctions to buy, but in reverse.There are two motives for buying: for a buyers own use or for resale. In thefirst case the value of the purchased good is the private value placed on it by theFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.100 PART 1 Power Market Fundamentalsbuyer. In the second case, the value is the price for which it can be resold. If thepurchase is for resale, then all potential purchasers will find the value to be thesame, i.e., the market price upon resale. This is called the common value.The Revenue Equivalence TheoremThe revenue equivalence theorem, a key result of auction theory, states thatthe four types of auction will all produce the same revenue if used in private-valueauctions. To help explain how this is possible, consider a comparison of a Vickrey(second price) auction and a sealed-bid (first price) auction.

Result 1-9.3 Four Types of Auctions Produce the Same RevenueThe four types of auctions, English, Vickrey, Dutch, and sealed-bid, all producethe same revenue if the bidders have private values. If they have common values,then their revenues are in the listed order with English producing the most.Assume the bids in each were $100, $200, and $300 by A, B, and C respectively.In each auction, C wins, but in the Vickrey auction, C would pay only $200 whilein the first-price auction, C would pay $300. This makes it seem that the revenueof the first-price auction is clearly greater by $100.The explanation of revenue equivalence involves the fundamental principleof rule design, Result 1-9.1. Changing the rules changes the behavior of the bidders.To analyze these behaviors assume that the bidders have private values correspond-ing to the above bids. First, consider bidder behavior under a Vickrey auction. Cwill bid $300 because he knows that if A and B have bid less he will win and getthe best possible price, the price of the next-highest bidder. If C loses, say to a bidof $305, he will be glad he lost, for winning would mean paying $305 for somethinghe values at only $300. If a bidder bids less than her valuation, she increases thechance of losing when she should win and saves no money. If a bidder bids aboveher private value her only extra wins from biding higher will be in auctions shewould rather lose. So all bidders bid their true values, and this design is incentivecompatible. Bidder C will win and pay the second price of $200.

Result 1-9.4 A Vickrey Auction Is Incentive CompatibleA second-price auction causes bidders to bid their true value, or if it is an auctionto purchase, they bid their true cost.Now consider a first-price auction. Bidding strategies depend on what is knownabout others bids. Assume that C knows that A and B almost surely have valuesof $100 and $200. Then C knows B will almost surely not bid higher than $200and perhaps lower. If C is sure enough he will bid $201 or less. So the revenueof a first price auction will be much less than $300 because C will not bid his truevalue. This auction is not incentive compatible. The calculation of bidding strategiesin such an auction is quite difficult, and it is remarkable that the revenue equiva-lence theorem can cut through this complexity and produce such a clean result.The winner in the first-price auction will pay $200 on average.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-9 Designing and Testing Market Rules 101One disadvantage of the first-price auction is the complexity of the optimalstrategy. Bidders are forced to guess the probability distribution of other bids andthen make a complex computation based on this guess. This introduces errors intothe bids. For example, in a power market, bidders in a Vickrey auction will bidtheir marginal cost and that will reproduce the standard merit order from whichthe system operator will dispatch generation efficiently. With a first-price auction,all generators with marginal costs below the expected market price attempt to bidjust under the market-clearing price. This produces a cluster of bids that have littleto do with the merit order and which differ more because of estimation errors thanbecause of costs. Dispatching the cheapest generators from this assortment ofbids will produce an inefficient dispatch.Revenue Equivalence and the Pay-as-Bid DesignIf the auction sells many units of the product, many megawatt-hours of power, andthere are many winners, then a second-price auction pays all winners the same whilea first-price, sealed-bid auction pays each winner his bid. This gives rise to the termssingle-price auction and pay-as-bid auction. Economists call a pay-as-bid auctiona discriminatory auction. As discussed in Section 1-9.1, FERC recently arguedfor replacing Californias single-price auction with a discriminatory auction onthe grounds that it would result in lower prices. If the auction under considerationwere buying a single indivisible unit of power of a known quantity, then the revenueequivalence theorem would prove that switching to pay-as-bid would have no affecton revenue, which means the average price paid would be the same.Unfortunately, electricity auctions are multi-unit procurement auctions in whichdemand is elastic and uncertain, and the revenue equivalence theorem does notapply. A paper by Frederico and Rahman (2001, 2) demonstrates that for suchauctions, in a competitive market structure, pay-as-bid reduces the price paid butalso reduces efficiency. They show that under monopoly conditions, the exerciseof market power is more difficult under pay-as-bid, and that firms with marketpower may react in inefficient ways to a switch to pay-as-bid thus reducingwelfare. They are also optimistic that under oligopolistic conditions pay-as-bid willsignificantly reduce market power but have not modeled this situation.These results are complex and ambiguous, and those who believe they see easyanswers have not understood the question. Theory may never yield definitiveanswers, and testing of auction designs may prove the only reliable method ofevaluation. Testing such a design for the first time in a 10 billion dollar per yearmarket may not be the most cost-effective approach.1-9.4 TESTING A MARKET DESIGNIn a turbulent environment such as the restructuring of the U.S. electric industry,new market designs are nearly always conceived and implemented without rigoroustesting. In fact a complete absence of testing is common; however, few designsare implemented without claims that they produce the correct incentives andFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.102 PART 1 Power Market Fundamentalsefficient outcomes. Unfortunately, when such designs are tested against eventhe most well-behaved hypothetical situations, they do not always live up to theirclaims.A moderately rigorous test would involve a laboratory simulation of the marketdesign. While this is recommended, especially when gambling with sums that canrun into the billions of dollars, a more modest course of testing is presented here.No design should be implemented without this minimal level of testing, which iscalled the bottom-line test because it tests the effect of a market design on thetotal cost of supply. It does not provide a cookbook procedure, but it provides astructure that is often missing, and it sets a minimum standard. The test procedurecan be broken into three steps.

Test The Bottom-Line Test of Market Rules1. Model the cost functions of the players in the market.2. Compute the minimum possible cost of serving the target load level.3. Compute the cost increase of serving the load under proposed rules.If consumer response to price (demand elasticity) is important for the rules beingtested, then the bottom-line test must be modified by examining the decrease intotal surplus caused by the design instead of the increase in cost. Fortunately, mostmarket rules can be tested adequately under the assumption of completely inelasticdemand. Then consumer benefit is unaffected by market rules and drops out ofthe test procedure. Occasionally, adding demand elasticity can simplify a modelby removing knife-edge discontinuities in behavior. In this case the net-benefittest should be used.Lack of demand elasticity confers market power on suppliers, and most designsare not efficient in the presence of market power. The bottom-line test is onlyintended to test designs for competitive markets, so to counteract the effects ofinelastic demand, suppliers should simply be assumed to behave competitively.The Least-Cost Focus of Economic TestingAs discussed in Section 1-5.2, least-cost production is the criterion for both shortand long-run supply-side efficiency. Statements about sending the right price signalsto generators, providing optimal incentives, and being efficient mean nothing ifthe design does not keep the delivered cost of production low. Conversely, if thedesign does minimize generation costs, it necessarily sends the right price signalsto generators and provides the right incentives. The supply-side implications of a competitive market design can be tested justby comparing the total cost of supply under the proposed design with the minimumcost of supply in an ideal world. The point is not that the ideal must be achievedbefore a design is approved, but the ideal provides a benchmark, and cost is thesole criterion. As simple as this test is, it can still include such complexities asenvironmental concerns by including their costs. (This is the only method ofinclusion that makes otherwise implicit trade-offs explicit.)February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-9 Designing and Testing Market Rules 1037. This might be termed an absolute impacted megawatt-mile approach and is a design that has beenproposed and inappropriately tested.The Advantage of Simple ModelsEconomic modeling is as much art as science, and mistaken conclusions result asoften from poor model design as from faulty calculation. Simple models minimizesuch errors. Those who prefer their ideas not be tested usually argue that simplemodels cannot test a design adequately and should not be used. Even when acomplex model is available, simple models should be used to check the reasonable-ness of the more complex models, and a simple model is always better than nomodel. Simple models can give clear-cut results when they are negative and can savethe considerable effort of a more elaborate test. One disadvantage, however, is thatwhile they can lend credibility to a design, they cannot serve as proof that it willsucceed in practice. That such testing can prove a design wrong but cannot proveit right may be discouraging, but it is always better to learn of failure during thedesign phase. 1-9.5 TECHNICAL SUPPLEMENT: EXAMPLE OF A BOTTOM-LINE TESTThis example demonstrates how to test a design with the bottom-line test and howto avoid spending a lot of money on complex tests when a design has an elementaryflaw. Detailed cost calculations are postponed to the end in order to focus onmethodology. This example was an actual proposed design, and the inappropriatetest was carried out. A Test of Two Transmission Charging RulesThe design to be tested consists of two rules that are intended to charge generatorsfor wires in such a way that new generators are induced to build in the optimallocation. The first rule specifies that the power flows caused by a generator arecalculated by assuming its power flows proportionally to every load on the system.(This is not a law of physics but only an accounting rule.) If a generator injects100 MW and there are two loads on the system, of 2000 and 3000 MW, then 20MW flows to the first load and 30 MW to the second, no matter where the two arelocated relative to the generator. Rule 1. Power is assumed to flow proportionally to every load.Rule 2. Flows are charged their proportional use of each lines capacity timesthe lines cost.Having used the first rule to compute the generators nominal power flow onevery wire in the system, the second rule is used to compute the charge for usingeach wire. The charge is based on the absolute value of the fraction of a linescapacity used each hour.7 In other words, if a generator causes a 20-MW flow ona 100-MW line with a fixed cost of $50/h, then the generator is charged $10/h noFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.104 PART 1 Power Market Fundamentalsmatter which way it sends power over the line. This completes the description ofthe design in question; these two rules are sufficient to compute the transmissionaccess charge for every generator. In all other respects the market is assumed tobe perfectly competitive. The stated purpose of the design focuses only on the linkage between this marketand the market for generation plants, and it ignores linkages to the energy market.Although these linkages deserve testing, for simplicity, the example will test onlythe effect of the rules on the location of new power plants.These rules were tested by constructing a model of all the power flows inthe state of California and computing them for every hour on every wire for a givenyear. Graphs were made showing how much power flowed on wires operating atvarious voltages. It was claimed that since most of the power flowed on high-voltagelines, and those were the ones being charged for, the market design would sendthe right signals. As a consequence of sending the right signals, investors wouldbuild plants in the right locations, and the market would operate efficiently. Butsuch testing misses the point. Notice that although some costs may have been calculated, no total minimumcost was calculated (step 2), and no total cost under the proposed design (step 3)was contemplated. The test did not rule out the possibility that generation costswould be double the economic minimum under the proposed market design. Thecentral economic question of cost minimization was simply not considered. Theseoversights are now remedied by applying the bottom-line test. Step 1: Modeling Costs and BenefitsBasic economics always assumes market participants will act to maximize theirbenefit net of costs, so cost and benefit functions must be specified to calculatethe predicted behavior. To perform a bottom-line test, first determine what costsand benefits are relevant. In this case, the relevant costs are (1) the cost of genera-tion including its dependence on location, and (2) the cost of wires. A usefuleconomic model must include both.Modeling elastic demand would complicate the computation of benefits andis not relevant to the benefits being claimed. The basic bottom-line test whichfocuses only on supply costs will be sufficient. The first test of a design shouldbe as simple as possible, and the model needs at least one wire and two generationlocations to evaluate the design. These are specified in the final sub-section whichuses the details of the model to compute costs.Step 2: Computing Minimum CostThe bottom-line test requires computing the minimum cost of producing anddelivering the power required to meet a fixed level of demand. In principle thiscan be done by trying all ways of producing the required output. Generally a littlemathematics will simplify the process. In the present example, the minimum costof delivered power is found to be $362,000/h. For a particular specification of thetest model, step 2 always gives a simple answer that is just one number. No excuseFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 1-9 Designing and Testing Market Rules 105should be accepted for a more complex or less precise answer although it may beuseful to test several variations of the model (each will have its own one-numberresult for step 2).Step 3: Computing Cost Under the Proposed RulesThe behavior of suppliers must be considered when computing the effect of therules on the total cost of delivered energy. Suppliers will react to market rules, andthis reaction must be predicted. Economics enters the test process at this point bydictating the assumption that suppliers will maximize their profits. This may notbe true when a rule is first put in place, but with practice, suppliers should learnhow to adjust their behavior to the rule and maximize their profit. The profitmaximizing assumption is key to economics, and though not precisely true, isgenerally the best approximation available.In the present model, taking into account the profit maximizing behavior ofgenerators, the total cost of delivered power will be $376,000/h. Step 3 shouldalways produce as simple an answer as does step 2.InterpretationThe result of this example can be summarized as a $14,000 (4%) increase in costcaused by the proposed rules. This might be tolerable, but a qualitative inspectionof the model raises more concerns. The rules cause all of the generation in thesystem to locate at the load center and consequently cause an eight-fold increasein the cost of transmission. This is unreasonable, and the rules should clearly berejected because they have failed such a simple and reasonable test.The benefit of the bottom-line test is dramatic. By applying it first, the expenseof a complex study can be saved. Additionally, it provides an intuitive understandingof the designs flaws that would be difficult to extract from a more complexsimulation. The following subsection builds the model and uses it to compute thecosts for steps 2 and 3, as well as to develop the intuition of the interpretation.Step 1: Building the Model and Computing Costs. Assume there are twocities in the market, and they are connected by a transmission line as shown inFigure 1-9.1. Assume for simplicity that generation can be located near either city,and the cost is the same: $10/MWh for capacity and $20/MWh for energy. Assumepeak load on the system is 16,000 MW with 12,000 MW located at city A and 4000MW located at city B. Assume the average hourly load is 10,000 MW, assume thatline capacity costs $4/MWh, and for reliability purposes assume the minimal linecapacity is 500 MW. This is a sufficient model of the relevant costs.Step 2: Finding the Minimum Cost. Because the above model assumes thatgenerators cost the same at either location, the cheapest arrangement is to locatethem where they are needed, that is 12,000 MW of generation at A and 4000 MWof generation at B. In this case, no power line is needed to facilitate trade. The totallong-run cost of power in this model is found by summing three components asfollows:February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.106 PART 1 Power Market FundamentalsFigure 1-9.1Minimum cost locationswith flows calculatedusing proposed Rule 2.16,000 MW$10/MWh =$160,000/h for generation capacity+ 10,000 MW$20/MWh =$200,000/h for energy+ 500 MW$4/MWh =$2,000/h for line capacityfor a total of $362,000/h. This is the minimum total cost of serving the load.Step 3: Finding Total Cost under the Proposed Rules Under the proposedtransmission pricing rules, generators will pay different transmission chargesdepending on their location. In particular, if they were located in the minimal costarrangement just described, the generators at A would have 1'4 of their flow assignedto the line from A to B because by Rule 1, 1'4 of it goes to the 25% of load at B.The generators located at B would have 3'4 of their flow assigned to that line. (Thissecond power flow is in the opposite direction and cancels the first, but this doesnot affect the charges.) Because charges are proportional to flow, the generatorsat B are charged three times more than the generators at A. Whenever a generatoris retired at B, it will be replaced with a generator at A because, counting transmis-sion charges, A is the cheaper place to locate.The long-run consequence of this dynamic is that all new generators will locateat A and all expansion of existing generators will take place at A. In the long run,all generating plants will be located at A. Consequently a 4 GW transmission linewill be built to supply Bs peak load. That is eight times bigger than the 500-MWline required for reliability in the least-cost configuration. This increases the totalcost of energy by the cost of the extra transmission line. An extra 3500 MW of linecosts an extra $14,000/h. This brings total cost under the proposed design to$376,000/h.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Part 2Reliability, Price Spikes, and Investment1 Reliability and Investment Policy2 How Price Spikes Recover Fixed Costs3 Reliability4 Limiting the Price Spikes5 Value-of-Lost-Load Pricing6 Operating-Reserve Pricing7 Market Dynamics and the Profit Function8 Requirements for Installed Capacity9 Inter-System Competition for Reliability10 Unsolved ProblemsFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.When, by building theories upon theories, conclusions arederived which ceaseto beintelligible,it appears timeto search into thefoundations of thestructureand to investigatehow far thefactsreally warrant theconclusions.Charles Proteus SteinmetzThe Education of Electrical Engineers1902Chapter 2-1Reliability and Investment PolicyRELIABILITY, PRICE SPIKES, AND INVESTMENT ARE DETERMINED BYREGULATORY POLICIES. Because these policies impinge on market structurerather than architecture, they have been overlooked too often as debates focusedon nodal pricing, bilateral trading, or on market rules. The result has been achaotic pricing policy and disaster in the Western U.S. markets. Part 2 assumesaway two major problems, market power and transmission constraints, to focusexclusively on the structural core of a contemporary power market. The goal ofPart 2 is to explain the major policy options and their implications. This requiresan understanding of the causal links between policy controls and the key marketoutcomesreliability, price spikes and investment. Both controls and outcomesare diagrammed in Figure 2-1.1.Supply and demand characteristics comprise a markets core structure, but ina power market these are unusually complex. The supply side cannot store its outputso real-time production characteristics are important, and two demand-side flawsinteract detrimentally with this characteristic. Consequently, the market cannotoperate satisfactorily on its own. It requires a regulatory demand for a combinationof real-time energy, operating reserves, and installed capacity, and this demandmust be backed by a regulatory pricing policy. Without this reliability policy, thepower system would under-invest in generation because of the demand-side flaws.Reliability policy is the part of the structural core that can be affected immediatelyby design. The demand-side flaws can also be affected by policy, but these designchanges take longer to implement.Without the demand-side flaws and reliability policy, Figure 2-1.1 wouldrepresent a normal market; demand and supply conditions would feed into themarket and determine prices. These would determine new investment which wouldFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-1 Reliability and Investment Policy 109Figure 2-1.1The structural core of apower market determinesreliability, price spikes,and investment. determine the supply conditions and reliability. When the demand-side flaws havebeen sufficiently ameliorated, short-run reliability policy will no longer be requiredto play its current role of providing the major incentive for long-run investmentin generating capacity. Price spikes will be controlled by demand elasticity andpower markets will operate normally. Chapter 2-4 discusses the threshold at whichthis becomes possible.Chapter Summary 2-1: Energy price spikes and, in some markets, installed-capacity prices induce the investment in generation which determines reliability.The duration of price spikes is roughly determined by accepted engineering rulesof thumb, but no engineering and no market determines the height of the spikes.Their height is determined by often-murky regulatory policies that limit what asystem operator will pay when the system runs short of operating reserve. Thus,neither determinant of investment, duration or height, is market driven.Many regulatory policies would produce the right level of investment, butpolicies that employ extremely high, short-duration price spikes should be avoidedbecause of their side effects. Such spikes cause investment risk, political risks, andincreased market power. Correctly designed policies can ameliorate these and otherside effects while inducing any desired level of investment.Section 1: Why Price Regulation is Essential. The second demand-side flawmakes it possible for customers to avoid long-term contracts and purchase in realtime fromthe systemoperator. Because the system operator sells at cost, its custom-ers will never be charged more than the systemoperators price limit. Consequently,they are not willing pay more in any market. If system operators had no policy ofpaying sufficiently high prices for enough hours per year, generators would notcover their fixed costs and would not invest. Thus, the market, on its own, wouldFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.110 PART 2 Reliability, PriceSpikes, and Investmentunderinvest and reliability would suffer. System operators do have pricing policies,and these determine the height and duration of price spikes.Section 2: The Profit Function. Regulatory policy determines the marketsprice when demand, including the regulated demand for operating reserves, exceedstotal available capacity. These price spikes determine the short-run profits ofgenerators, and the expectations of these profits induce generation investment.Investment increases installed capacity (ICap), which reduces both price andprofits. This feedback loop (shown in Figure 2-1.1), which is controlled by reliabil-ity policy, determines the equilibrium level of ICap and thus long-run reliability.The profit function summarizes the information needed to find the equilibriumICap level. It takes policy into account and plots expected short-run profits (ofpeakers, for example) as a function of ICap. The equilibrium ICap level occursat the point on the profit curve where short-run profits just cover the fixed costsof peakers. The short-run profit function derived from the combination of energyand capacity prices shows what level of ICap and reliability a given set of policieswill produce.Section 3: Side Effects of Reliability Policy. Many different policies producethe same optimal level of ICap and reliability, but they have different side effectsaccording to the steepness of their profit functions. A steeper profit functionincreases risk and facilitates the exercise of market power. By choosing policiesthat produce low, long-duration price spikes, a flatter profit function can beachieved.Section 4: Inter-System Competition. Competition between systemoperatorsmilitates against low price spikes. Any system operator with a low price limit onenergy and reserves will find its operating reserves purchased out from under itat crucial times. Regional coordination of pricing policies can avoid such competi-tion and its negative side effects.Section 5: Demand-Side Effects of Price Limits. The ideal solution to theinvestment/reliability problem would be sufficient price elasticity to keep themarket-clearing price well below the value of lost load at all times. A high pricelimit encourages demand elasticity, but this consideration must be weighed againstthe increased risk and market power associated with high limits. A better solutionmight be to price demand and supply separately during price spikes.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-1 Reliability and Investment Policy 1111. See also Ruff (1999, 28), and FERC (2001b, 4).2. Some will object that for the last few percent of supply, marginal cost climbs rapidly to unlimitedheights as wear-and-tear and the possibility of significant damage increases in the emergency operatingrange. This is correct, but it does not solve the present dilemma. These marginal costs cannot provide abenchmark for setting the market-clearing price when demand exceeds supply. They are not verifiable, andeven if they were, just before the market fails to clear they easily exceed the value of power to consumers,VOLL. If price were set to the last marginal cost before failure, consumers would pay more than the poweris worth and stimulate overinvestment in generation. Chapter 2-4 also discusses the possibility of usingthe high demand-sided bids, found in some more advanced markets, to set price. This is similarlyinappropriate.2-1.1 PRICE REGULATION IS ESSENTIALThe second demand-side flaw, the system operators inability to control thereal-time flow of power to specific customers, necessitates the regulators role insetting prices (see Section 1-1.5).1 Without this flaw, the system operator couldsimply enforce contracts. Instead, it must buy power to balance the system andmaintain reliability.Although the system operator must play an active role in present systems, thatrole might be restricted to setting a price that equated supply and demandin otherwords, a price that cleared the market. If this were possible, the system operator,though active in the price-determination process, would have no control over priceand would not be a price regulator. In most hours of the year, the system operatordoes play such a passive role.Because of the first demand-side flaw (a lack of real-time metering and billing)demand is so unresponsive to price that a simple market-clearing role is not possiblein all hours. If installed capacity is at an optimal level or lower, there will be timesduring which demand exceeds supply and load must be shed. NERC estimates thiswill happen for about 1 day out of 10 years. At such times, no price will clear themarket. The system operator could continue to pay the highest nominal marginal cost(left-hand marginal cost) of any generator after the market failed to clear. Thiswould still constitute regulatory price setting, but it would be a minor intervention.With only this minimal intervention, investment would suffer a serious decline.The competitive market-clearing price, when supply exceeds demand, is the physicalmarginal cost of generation which is usually less than $200/MWh.2 For this priceto support investment in new peakers, demand would need to exceed supply (forcingblackouts) for more than 200 hours per year, not the 2.4 hours that NERC considersoptimal.

Fallacy [2-4.1] The Market Will Provide Adequate ReliabilityContemporary markets, with their demand-side flaws and negligible demandelasticity, would grossly underinvest in generation without regulatory pricesetting.The minimal price intervention that would produce a reasonable level ofreliability is known as value-of-lost-load (VOLL) pricing. This has been studiedFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.112 PART 2 Reliability, PriceSpikes, and Investment3. The outcome is optimal provided VOLL is set correctly. Although this is extremely difficult to estimate,Section 2-5.4 shows that market efficiency is not too sensitive to misestimation and that there is no moreaccurate method available for determining the optimal amount of reliability.4. The aggregate price spike is defined in Chapter 2-2, and is the upper part of the annual price-durationcurve.Whats a Regulator to Do?Prices must spike to pay the fixed costs of genera-tors, or there will be no new investment. The highestprice should occur when load has been shed, buteven then the system operator should pay no morethan the power is worth. Academics estimate this tobe more than $1000/MWh but less than $100,000.The market gives no answer. Australian regulatorspick a value near $10,000 and thereby determineinvestment.U.S. regulators, correctly wishing to reducemarket volatility, choose a lower price limit and paythat price when reserves are low not just when loadis shed. FERCs price limit and NERCs operating-reserve requirements combine to determine thelong-run investment incentivesnot by design but bychance.When the demand-side is fully functional,elasticity-based price spikes will correctly determineinvestment. Spikes will be low and broad and themarket stable. Present policy should seek to mimicthis long-run, fully-functioning, competitive behavior.Policy should not deliberately mimic the volatility ofa market with a demand-side that is still 98% frozen.and implemented by Australias National Electricity Market (NECA, 1999b). Thisapproach recognizes that the system operator must purchase power on behalf ofload when demand exceeds supply and instructs it to pay VLL, the value of additionalpower to load, whenever some load has been shed (during a partial blackout). Thisis sensible, and ignoring risk and market power and given the first demand-sideflaw, it produces an optimal outcome.3 It induces exactly the right level of installedcapacity, which minimizes the sum of the cost of that capacity and the cost of lostload.Implementing VOLL pricing requires a regulatory determination of VLL becausethe market cannot determine it. This value will determine the height of the aggregateprice spike, and the duration of the price spike will be determined by the regulatorsdecision to set this price when, and only when, load has been shed.4 The Australiansestimated VLL to be about $16,000 US but set their price limit at only about$10,000 US. Both the height and average annual duration of the price spikes underVLL pricing are determined by regulatory policy and not by any market mechanism.In the United States, system operators take a differ-ent approach. In compliance with NERC guidelines,they set operating reserve requirements which coverregulation, spinning reserves and nonspinning re-serves which together amount to roughly 10% of load.Instead of waiting until load must be shed to raiseprice, a shortage of operating reserves is deemed to besufficient reason to pay whatever is necessary. Thisresults in high prices whenever demand exceeds about90% to total available supply, an occurrence far morecommon than load shedding. In this way, U.S. reliabil-ity policy determines a much longer duration for pricespikes.Determining the height of energy price spikes ismore complex because system operators compete forreserves. If one operator is willing to pay a high price,it can buy up the reserves of its neighbor and therebyforce it to pay a high price to acquire its own reserves.This complication is discussed in Section 2-1.4, butthe essence of regulatory pricing is better understoodby considering a single isolated market.The engineering approach considers requirementsfor operating reserve to be sacred and avoids assigninga maximum price that should be paid to comply withthem. The suggestion is to pay what is necessary.Before markets, this caused no problems, but when prices exceed a few thousandFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-1 Reliability and Investment Policy 113The Price-Cap Resultdollars per megawatt-hour, system operators understandably begin to have secondthoughts.As a result, all four ISOs have requested FERCs approval for price caps.These are often, and more accurately, termed purchase-price caps. In fact they aresimply limits on what the system operator will pay in order to comply with require-ments for operating reserve. They are not price caps or price controls of the typeimplemented in other markets. They do not tell a private party that it cannot chargeanother private party more than Pcap. System operators are not allowed to makea profit, so they charge only as much as the power costs them, which is never morethan their price limit. Because of the second demand-side flaw, when the systemoperator refrains from paying more than a certain price limit, no private party willpay more as it can always take power in real time without a contract.

Result [2-4.6] The Real-time Price Limit Effectively Caps the Entire MarketIf a system operator never pays more than Pcap then it will never sell power formore. Because of the second demand-side flaw, customers of the system operator(typically, load serving entities) can always wait and purchase power in real timefor Pcap or less. Consequently, they will never pay more in any forward market,and all power prices are, in effect, capped at Pcap.Purchase-price limits, openly implemented by the system operator, typicallydetermine the highest market price for the real-time market and for all forwardmarkets, but it is not unusual for the system operator to make out-of-marketpurchases at prices above the official price cap. These prices are not determinedby the market because the demand for out-of-market purchases is typically causedby operating reserve requirements.While there are sound engineering reasons for operating reserve requirements,these reasons do not extend to price determination. In particular, they do not sayoperating reserves are worth $2,000/MWh or any similar value whenever the reserverequirement is not met. Any price paid out of market is set by some regulatory,nonmarket process no matter how informal that may be.In conclusion, the limits on what a system operator will pay for power cannotbe set by the market. They are set by complex processes that sometimes involveformal regulation and sometimes involve judgments by system operators. In anycase, the high prices paid for reserves determine through arbitrage the prices inother markets (see Sections 1-8.3 and 2-4.5). Thus, system-operator policy deter-mines the height of price spikes in all submarkets of a power market. Whetherinvestment is induced purely by market-driven price spikes or by a regulatoryICap requirement, it is, in reality, primarily determined by a regulatory policy.Neither approach is more market-based than the other.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.114 PART 2 Reliability, PriceSpikes, and Investment5. If prices are not capped and demand is too inelastic, there may be no equilibrium.The Regulatory-Price-Spike ResultResult [2-4.4] Regulatory Policy Determines the Height and Duration of Price SpikesBecause of the second demand-side flaw, markets will not set energy priceshigher than the system operators price limit. Consequently this regulatory limitdetermines the height of price spikes. The average annual duration of spikes iscontrolled by the application of this limit to the operating reserve requirement.The essential difference between the Australian and the United States approachesto the determination of price spikes is not that U.S. spikes are lower and of longerduration. The key difference is that Australia has determined the shape of its pricespikes deliberately by calculating what is required to produce an installed-capacitylevel that will produce a target reliability level (some three to five hours per yearof load shedding). The United States has made no such effort. In fact, price-spikeduration is set by short-run engineering considerations, while the height of spikesis typically set by a political process that is concerned mostly with market power.Very roughly, NERC controls the price-spike duration, while FERC controls theheight. But NERC regional adequacy and operating reserve criteria do not considercosts (Felder 2001) and FERC does not consider operating reserve limits whensetting price caps. In addition, capacity requirements are often added to the marketwithout any thought for how these mesh with the defacto price-spike policy. Inshort, Australias approach is deliberate, while the U.S. approach is a matter ofchance.2-1.2 THE PROFIT FUNCTIONProfit drives the investment that is key to the market equilibrium described by Figure 2-1.1. The core of that equilibrium process is the loopof causal links from the market through prices, investment, installedcapacity and back to the market. This circularity determines a long-runmarket equilibrium.5 If prices are high, investment will be encouraged,and installed capacity will increase. With more ICap, prices will fall. The systemis in equilibrium if ICap,combined with exogenous factors, causes prices that are just profitableenough to cover the fixed costs of the installed capacity.Energy and capacity prices both contribute to profit and thus help determinethe equilibrium level of ICap. Because separate policies affect energy and capacityprices, these must be coordinated if the right level of ICap is to be induced. Theintermediate goal of these policies is to produce the right profit level at the rightlevel of installed capacity, and the combined effect of energy and capacity priceson profit is what matters. This combined effect is computed by finding the profitfunction produced by each policy and summing the two functions.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-1 Reliability and Investment Policy 1156. See Chapter 1-3 for an explanation of units. $/MWh can be converted to $/kW-year by multiplying by8760'1000.

Result [2-8.1] Energy and Capacity Prices Together Induce InvestmentInvestment responds to expected short-run profits, which are determined byenergy prices and (if there is an installed-capacity requirement) by capacityprices. Regulatory policies determining these prices need joint consideration.A profit function plots expected profits as a function of the ICaplevel. A low ICap level produces shortages and high energy prices whichprovide a high profit level. When ICap is high, shortages are very infre-quent and prices are rarely high. This leads to a low expected annualprofit. At some level in between, expected prices are just high enoughto produce a profit level that would cover the fixed cost of a new peaker,about $6/MWh of installed peaker capacity.6 This is the equilibrium levelof ICap, Ke.The figure at the left shows a profit function for a peaker derived fromenergy prices. As ICap drops below the equilibriumlevel, profits increaserapidly, and as it rises above the equilibrium level, shortages of capacitybecome rare and profits rapidly fall to zero. In most markets they fallto zero much more quickly than shown. The precise shape of this curvedepends on reliability policy, on the nature of demand fluctuations, the frequencyof generation outages and on demand elasticity. The important points are that thecurve depends on regulatory policy and the curve can be calculated.An installed capacity requirement produces a very different profitfunction. When ICap is below the required level, ICap-profits for allgenerators are set by the ICap-requirement penalty, and when ICap isabove the required level, profits are zero. (A small correction shouldbe made for market power.) Adding profit from the energy market toprofit from the capacity market produces a total profit function fromwhich an equilibrium value of ICap can be determined.The equilibrium value of ICap, Ke, is not automatically the optimalvalue. Policy must be adjusted so that the profit function of a peakercrosses the profit level (approximately $6/MWh) required to cover thefixed costs of a peaker at the optimal ICap level. Any profit functionthat does this, no matter what its shape, will induce the right level ofICap. Thus there are many optimal policies to choose from. Availablepolicy parameters include the system operators price limit when load is shed, theprice limit when operating reserve requirements are not met, the required levelof operating reserves (which can be increased), the required level of installedcapacity, and the penalty for being short of capacity.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.116 PART 2 Reliability, PriceSpikes, and Investment7. Long-termcontracts between new generation and load can reduce this risk premium, but, so far,long-termcontracting has meant only 2 or 3 years in most cases and the equilibriumlevel of contract coveris still unknown.

Result [2-6.1] Many Different Price Limits Can Induce Optimal InvestmentIf the system operator pays only up to Pcap but no more any time operatingreserves are below the required level, a low value of Pcap will suffice to inducethe optimal level of installed capacity. The higher the reserve requirement, thelower the optimal price limit will be. Capacity requirements can further reducethe optimal level of Pcap.One other policy choice deserves attention. The engineering notion of anabsolute reserve requirement, which worked well under regulation, makes littlesense in a market. The demand for operating reserves, like the demand for anythingelse, should be described by a downward-sloping demand function. The fewer themegawatts of reserves, the more they are worth. Introducing such a demand functionincreases policy choices and has the added advantage of increasing the elasticityof demand in a market where even small increases matter.2-1.3 SIDE EFFECTS OF RELIABILITY POLICYMany policies will produce a profit function that determines the correct equilibriumlevel of installed capacity, but this does not mean they are all equally desirable.The first goal is the correct average level of installed capacity, but that is not theonly criterion for a well-functioning power market. If ICap is right on average butfluctuates too dramatically, the excess unreliability in years of low ICap will morethan offset the excess reliability in years of high ICap. In fact any value of ICapother than the optimal value causes a reduction in net benefit, so no matter whatthe average value, fluctuations produce a sub-optimal result.But two phenomena other than reliability deserve attentionrisk and marketpower. Even if the ICap were exactly right every year, so that reliability wasoptimally maintained, profits would fluctuate. The profit function only recordsexpected, or average, profits. Actual profits can vary dramatically. A 2% increasein demand is equivalent to a 2% reduction in ICap in terms of its effect on profit.So if the profit function can be very steep at the equilibrium, any small unexpectedincrease in demand will cause a large increase in profits.A VOLL pricing policy is designed to produce about three hours of extremelyhigh prices (equal to VLL) every year. But some years, unusual weather, generatoroutages, or unexpected demand growth will cause 10 or 20 hours of VOLL pricing.If ICap has been set correctly, then profits must average out correctly which impliesthere must be five years of zero profits for every year with 18 hours of high prices.Ten years of zero short-run profitslosses, from a business perspectivewouldnot be out of the question. Investors will consider such a market very risky andwill demand a risk premium for investing in it.7 Moreover, because building powerplants takes years, 2 high-profit years might well occur consecutively. In this case,February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-1 Reliability and Investment Policy 117there may be political repercussions from the observation of high profits coupledwith the pain of high prices.A profit function that is extremely steep also encourages the exercise of marketpower. Withholding 2% has the same impact on profits as a 2% reduction in ICap.So profit functions that are very steep reward withholding most handsomely. Again,the VOLL pricing policy fits this description.A flatter (less steep) profit function can be obtained by designing price spikesthat are lower and of longer duration. Instead of $15,000/MWh for 4 hours per year,one can design price spikes that reach only $500/MWh for 120 hours per year. Thiswould be done by setting a purchase price limit for the system operator of $500and requiring that it be paid whenever the system was short of operating reserves(instead of waiting until an actual blackout). If this still does not produce high pricesfor 120 hours per year, the operating reserve requirement could be increased.In addition, part of the fixed costs can be recovered from the capacity marketif the correct capacity requirement and the penalty are implemented. If half the fixedcost is recovered in the capacity market, the height of price spikes can be cut inhalf for any given duration of high prices. Some policy combinations produce flatterprofit functions and these reduce risk and the exercise of market power. If properlydesigned, these policies will cause no reduction in the equilibrium level of installedcapacity. Consequently, it is the side effects of reliability policy, risk and marketpower, which should determine the structure of the policy and thus the shape ofthe profit function.

Result [2-6.4] Reliability Policy Should Consider Risk and Market PowerThe right average installed capacity will provide adequate reliability, but two sideeffects of reliability policy should also be considered. Infrequent high price spikesincrease uncertainty and risk for investors. This raises the cost of capital and, inextreme cases, causes political repercussions. The possibility of extremely highprices also facilitates the exercise of market power.2-1.4 INTER-SYSTEM COMPETITIONConsider an isolated competitive market in which $200/MWh is sufficient to callforth all available operating reserves. Suppose $500/MWh is sufficient to purchaseall power available from these sources during an emergency. As these prices aretoo low to stimulate the appropriate level of investment given most operating reservepolicies, the systemoperator has imposed an ICap requirement and enforced it witha moderate penalty. This provides capacity owners with an additional source ofprofits, which is just sufficient to induce optimal investment.This policy provides a relatively smooth profit function which reduces risk forinvestors and discourages the exercise of market power. While engineers mayconsider $200/MWh an inadequate effort to buy reserves at any cost, the factremains that a higher price would procure no more in the short run. Even a supplierwith market power would not withhold reserves in the face of a firm price limit,February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.118 PART 2 Reliability, PriceSpikes, and Investment8. It may be suggested that under some emergency agreement systemA would allow systemB to purchasepower fromsystemA, thereby avoiding load shedding by B and reducing As reserves below its requiredlevel. But this implies that As reserves are in effect also Bs reserves. In this case, there is no reason foreither to spend extra on reserves as long as it knows the other will purchase themand share them. Thiscontradicts observed behavior of systemoperators who do pay extra to obtain their own reserves.because there would be no possibility of profiting froma price increase. In the shortrun, paying more would not increase reliability, and, in the long run, it would onlyserve to increase it above the optimal level.If this isolated market were connected to another, identical, market, theseconclusions would change. Now both markets will find that they can increaseshort-run reliability by paying more for operating reserves. When reserves are short,say only 5% instead of the required 10%, either systemcan obtain a full complementof operating reserves by outbidding the other.To be specific, assume each market has 10,000 MW of load and 10,500 MWof capacity, but systemA has purchased 500 MW of operating reserves from systemB as well as 500 MW of reserves from its own suppliers. System B now has zerooperating reserves while systemA has its required 10%. Suppose a generator selling500 MW of power to market B experienced a forced outage. Market B will thenbe forced to shed 500 MW of load. A similar outage in Market A would cause onlya reduction of operating reserves from 1000 to 500 MW.8By bidding above market Bs price limit and purchasing its reserves, marketA has increased its reliability, something that was impossible when the two marketswere isolated and not in competition. Of course, market B will soon realize whathas happened and retaliate by bidding above As price limit. The end result of suchcompetition will be high limits on the price of operating reserves and energy. Thiswill make the profit functions steep and will increase risk and facilitate the exerciseof market power. This outcome was acknowledged by FERC in its July 2000 rulingapproving identical price caps of $1,000 for the three Eastern ISOs. It correctlyruled against a $10,000 price cap for the NY ISO on the grounds that this wouldtend to undermine PJ Ms $1,000 price cap.

Result [2-9.1] Competition Between System Operators Induces High Price SpikesIf two markets with different price spike policies trade energy and operatingreserves, the one with higher price spikes will gain in reliability and save moneyrelative to the other. This will force the low-spike market to use higher pricespikes. If regional price limits are not imposed, inter-system competition will leadto reliability policies with undesirable side effects.2-1.5 DEMAND-SIDE EFFECTS OF PRICE LIMITSLow, long-duration price spikes can induce the same optimal level of installedcapacity as high narrow price spikes, but the side effects of risk and market powerwill be reduced. Besides these supply-side effects which argue against high pricespikes, there is a demand-side effect that argues for high price spikes. High pricesencourage price responsiveness both directly and through learning. Some loadsFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-1 Reliability and Investment Policy 119will not find it worth curtailing their use of power until prices exceed $1,000/MWh.But, once a load has learned to respond, it may find it sensible to respond to priceincreases that would not trigger a response before the necessary control equipmentis installed and such responses become routine.Although these effects are important, they do not negate the conclusions basedon the supply-side effects, though they suggest a trade-off. The demand-sideresponse obtained by utilizing extremely high price spikes with no warning timemay be little more (or even less) than the demand response obtained by lower, morefrequent price spikes. These may be more readily anticipated by day-ahead markets,thereby giving loads a days lead time to plan their response and implementcost-mitigating procedures.Another possibility is to set demand-side prices higher than supply prices duringprice spikes. This would require a balancing account to keep the two revenuestreams equal in the long-run, but that is a simple matter.A similar problem arises from the possibly high prices required to wring thelast MW of production out of generators. The price of power supplied by generatorsoperating in their emergency operating range could be exempted from the normalenergy price limit. Suppose the normal energy price limit were $500/MWh, andthe maximum output at this price fromgenerator G were 400 MW over the previousyear. Then any output above 400 MW could be subject to a price limit of$2,000/MWh, without significantly steepening the profit curve.Once the ideas of calculating profit curves and considering the side effects oftheir shape have been understood, many design possibilities can be considered andevaluated. In the long run, when demand has become quite elastic even in theextremely short timeframes needed to replace spinning reserves, these designconsiderations will no longer be needed. Before that time, much can be gained bytaking full advantage of the multitude of policies compatible with an optimalaverage level of installed capacity. A pricing policy should be selected from amongthese based on its ability to minimize the collateral damage from risk and marketpower.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. Power markets are termed competitive if their supply side is competitive even when demand-sideflaws prevent the market fromdetermining competitive prices.Indebtedness to oxygenThechemist may repayBut not theobligationTo electricity.Emily Dickinson(183086)The Farthest Thunder That I HeardChapter 2-2Price Spikes Recover Fixed CostsWHAT PRICES WILL COVER A GENERATORS FIXED COSTS WITHOUTOVERCHARGING CONSUMERS? Short-run competitive prices perform thisservice and, in addition, induce the right level of investment in every type ofgeneration technology. This does not solve the long-run problems of power marketsbecause demand-side flaws prevent contemporary markets from determiningcompetitive prices.1 Subsequent chapters will discuss regulatory policies thatcompensate for these flaws, while this chapter focuses on how competitive powermarkets will work once the flaws are eliminated.Although not completely accurate, competitive analysis is useful for dispellingtwo fallacies concerning fixed costs. The first asserts that prices equal to marginalcost (competitive prices) cannot cover fixed costs. The second asserts that althoughthey can, they will do so only when the market is seriously short of capacity.Chapter Summary 2-2: Short-run competitive prices would recover fixed costsfor peakers and baseload plants alike. They would stimulate investment in the mixof technologies that produces the required power at least cost. Demand will occa-sionally push prices well above the average marginal cost of any supplier but notabove the right-hand marginal cost. These price spikes can be summarized witha price-duration curve that facilitates computation of the competitive outcome.Section 1: The Fixed-Cost Fallacy. This fallacy asserts that short-run competi-tive prices (marginal-cost prices) will prevent generators fromrecovering their fixedcosts. These are covered not because short-run competitive forces set price equalto marginal cost, but because, if they were not covered, investors would stopbuilding plants while demand continued to grow. This would cause shortages andFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-2 PriceSpikes Recover Fixed Costs 121The Fixed-Cost Fallacyhigher prices. The long-run competitive forces ensure price spikes will be highenough to cover fixed costs. This dynamic is very robust and works even with aprice cap. Once a lack of investment causes shortages, the lower price spikes willlast long enough to cover fixed costs.Section 2: Optimal Price Spikes for Peakers. The weak version of theFixed-Cost Fallacy asserts that marginal-cost prices will be high enough to coverfixed costs only because of a shortage of installed capacity. A model that includesfluctuating demand, two kinds of generators, and marginal-cost prices shows thatinvestors will minimize the total cost of production by building the right amountand right mix of generation. Individual price spikes can be summarized by the priceduration curve. The portion of this curve that lies above the variable cost of a peakeris called the aggregate price spike, and it measures the annual scarcity rentsreceived by peakers.Section 3: The Lumpiness of Fixed Costs. Fixed costs would not be lumpyif generators could be scaled down as much as desired, but a 10-MW coal plantis not 50 times cheaper to build than a 500-MW coal plant. In effect, generatorscome in discrete sizes or lumps. When a fractional number of plants is optimal,lumpiness interferes with the efficiency of competition. This inefficiency declinesin proportion to the square of the number of plants in the market with the resultthat it is entirely negligible for markets of even modest proportions.2-2.1 THE FIXED-COST FALLACYA common fallacy asserts that if a generator always prices output at marginal costit will fail to cover its fixed costs. This notion is based on the true observation thatin the normal output range, marginal cost is always less than the long-run averagecost of generation including the cost of the plant's capital investment. Section 1-5.3refutes the fallacy in a general context, and the argument presented there applieswithout modification to the power industry. But the fallacy causes enough confusionto warrant restating the analysis in the context of the wholesale power market.The Fixed-Cost Fallacy should not be confused with the true proposition thatwhen generating capacity is excessive, competition will cause generators to failto cover their fixed costs. This is not a problem with competition or with electricitymarkets. This is the way Adam Smith's "invisible hand" signals that there shouldbe no new investment.

F FF Fallacy allacy allacy allacy 2-2.1 Marginal-Cost Prices Will Not Cover Fixed CostIf the price paid to generators always equals their (physical) marginal cost, theywill fail to cover their fixed costs.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.122 PART 2 PriceSpikes, Reliability, and Investment2. Short-run profit is less than scarcity rent when startup and no-load costs are taken into account, butthose are ignored in Part 2.Figure 2-2.1Continuous marginalcosts and a nearly flat(elastic) demand curvefor one supplier.Modeling a Generator Generators will be assumed to have continuous supplycurves that are extremely steep in the final emergency operating range which startsat their maximum, or full, output level (see Figure 2-2.1). This model producesthe same results as one using a truly vertical supply curve but has the advantageof being more realistic with a well-defined marginal cost at all levels of supply.(Readers unfamiliar with the treatment of marginal cost when demand intersectsa vertical supply curve should review Chapter 1-6.) The constant value of marginalcost to the left of full output will be referred to as the generators variable cost.Startup costs will be ignored throughout Part 2.The demand curve faced by a single supplier in a competitive market is simplya horizontal line at the market price. At any price above the line, demand for asuppliers output is nil, while at any below-market price demand is much more thanthe suppliers maximum possible output. Such a demand curve is shown inFigure 2-2.1, but a small slope is added for realism. In most markets the price anindividual supplier can charge is at least a little sensitive to its output.How Generators Earn More than Variable Costs. Because supply equalsdemand, the supply in Figure 2-2.1 is Q, and at that point marginal cost has risento equal price, P. But the first MWh produced, and each succeeding MWh up tomaximum capacity, has a cost of less than half that much. As a consequence,average variable cost is about half of P.Figure 2-2.1 also shows that revenue, R, is exactly P Q. Because revenue isgreater than total variable cost, TVC, the generator has money left over to coverfixed costs. This is termed short-run profit, scarcity rent, or more technically,inframarginal rent. (Section 1-6.1 discusses scarcity rent.)2Scarcity rent =short-run profit =R !! TVCIf the market price is high enough, the generator will cover its fixed costs, butif the market price is too low, it will not. The real-world situation may seem morecomplex because prices fluctuate, sometimes dramatically, but this changes little.If the average price is high enough, the generator will cover its fixed costs, and,if not, it wont. The only question is what determines the average market price.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-2 PriceSpikes Recover Fixed Costs 1233. Chapter 2-6 considers the problemof excessive fluctuations in the short-run profit level and the levelof investment. Large enough fluctuations will cause significant inefficiencies even if capacity is right onaverage. Investors can also over- or under-collect total fixed cost for a project if there are technologicalsurprises after the plant is built; but on average, fixed costs will be recovered. Why the Competitive Price Exactly Covers Fixed Costs. If marginal-costprices did not cover fixed costs, investors would choose to build no more generators.As demand grew and generators wore out, the market would tighten causing priceto rise. On the other hand, if marginal-cost prices more than covered fixed costs(which includes a normal risk-adjusted rate-of-return on capital) investors wouldbuild generation, supply would outstrip demand, and the price would fall. Whenthe market price more than covers fixed costs, price declines; when price fails tocover fixed costs, it increases. Consequently, price converges toward the point atwhich fixed costs are exactly covered. Once there, it has no inherent tendency tochange.Frequent external disturbances, such as changes in demand or the opening ofa new plant, push the market out of equilibrium. But investors make their bestestimates of what will be needed, and they err on the high side as often as they erron the low side. Although marginal-cost prices do not exactly cover fixed costsat all times, they cover them on average. This is all that can be expected and allthat is needed.3

Result 2-2.1 In the Long-Run, Suppliers Recover Their Fixed CostsIn a long-run competitive equilibrium, generators recover their fixed cost and nomore, even though price equals physical marginal cost (P =MC) at all times andfor all generators. Revenues that help cover fixed cost are call short-run profits.Result 2-2.1b Restatement for Supply Curves with Vertical SegmentsIn a long-run competitive equilibrium, generators recover their fixed cost, eventhough the market price is competitive and satisfies MCLH<

P <

MCRH at alltimes and for all generators (see Section 1-6.3).This discussion of fixed-cost recovery does not depend on any of the detailsof cost functions or even on the market being short-run competitive. It dependsonly on the ability of generators to enter and leave the market. Consequently, theresult holds automatically for all of the upcoming models and for all of theirgeneralizations to more complex cost structures. It only fails if there are barriersto entry. Then the generators recover more than their fixed costs; they recoverenough to pay for crossing the barrier.2-2.2 OPTIMAL PRICE SPIKES FOR PEAKERSThe previous section showed that competitive prices will cover fixed cost, but thatdoes not prove them optimal. A weaker version of the Fixed-Cost Fallacy admitsthat long-run forces will ensure that fixed costs are covered, but it claims this wouldlead to a serious shortfall in generation capacity under competitive pricing. ThisFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.124 PART 2 PriceSpikes, Reliability, and Investment4. According to Table 2-2.1, if a 5-MW base-load plant is used for 100 hours to produce 200 MWh ofenergy, the total cost in dollars will be 510012+20018.Figure 2-2.2Two technologyscreening curvesshowing capacity factorsfor which eachtechnology is optimal.section models a market with two kinds of generators and fluctuating demand. Itshows that price spikes caused by short-run market clearing induce the right levelof investment for both technologies even though they face the same market-clearingprices. This result extends to any number of technologies.The Two-Technology ModelThe Supply Side. The supply-side of this market is modeled as having twoavailable technologies, base-load generators and peakers with costs as shown inTable 2-2.1.Table 2-2.1 Costs of Available TechnologiesTechnologyFixed Costper MWhVariable Costper MWhPeaker $6 $30Baseload $12 $18Note that fixed costs have been expressed in the same units as variable costs.4 Asexplained in Chapter 1-3, this is necessary for constructing the screening curveswhich are presented in Figure 2-2.2.Screening curves, described in Sections 1-3.3 and 1-4.2, plot the total cost ofgeneration as a function of the generators capacity factor, its average output dividedby its maximum output. (This is not the average cost of the energy produced, butthe average cost of the capacity used.) If the generator produces nothing, then totalcosts equal fixed costs, which means the screening curve starts out at the level offixed costs. As the capacity factor of a generator increases, the total variable costof output increases proportionally and is added to fixed costs to produce thescreening curve, a linearly increasing total cost curve. The plotted cost is the averagehourly cost of a MW of capacity utilized at the indicated capacity factor. Thesecurves can be used to decide which generator is the cheapest source of power toserve load for any given duration because serving a load of duration D results inFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-2 PriceSpikes Recover Fixed Costs 125Figure 2-2.3Supply and demand forthe two-technologymodel.a capacity factor, cf , equal to D. For example, in Figure 2-2.2, the peaker technologyis cheaper for all loads with duration less than 0.5 (4380 hour/year), while thebase-load technology is cheaper for all loads with durations greater than 0.5.The Demand Side. Two types of information concerning demand are needed:load duration and price elasticity (see section 1-4.1). Figure 2-2.3 illustrates ademand curve that shifts back and forth daily relative to one possible supply curve.Demand shifts in a linear manner that makes it equally likely to be found at anylevel from 4000 MW to 8000 MW, assuming it is not curtailed by a high price.The load-duration curve of Figure 2-2.4 depicts the interaction of supply anddemand. The flat spot at the top of this curve occurs if available capacity is lessthan 8000 MW, which will prove to be the case in equilibrium. Once generatingcapacity is exhausted, demand is limited by high prices. This is possible becausethe present chapter assumes that demand is sufficiently elastic to clear the marketat all times as is required for a competitive market.The flatness of the demand curve at $1,000/MWh is unrealistic, as a real demandcurve would be downward sloping. It could be interpreted as a price-capped market,but, in this model, it is used only as a simplification that has no impact on thequalitative results. The horizontal portion should be interpreted as demand elasticitythat is reflective of the value of power to consumers. They simply do not want anypower if it costs more than $1,000/MWh.The Regulatory SolutionFaced with this market, the traditional regulatory solution would be to set priceto average cost, build enough generation capacity to cover the full 8000 MW ofpeak demand, and use the screening curves to determine that 6000 MW shouldbe base-load capacity and 2000 MW should be peak capacity. This last conclusionis determined by reading the screening curves to find that the trade-off point is ata duration of 0.5 and then reading the load-duration curve to find that, at thisduration, load is 6000 MW.The regulatory solution finds the optimal level of baseload capacity but setstoo high a level for peaker capacity. Regulators have traditionally set price ataverage cost and this has prevented high prices from dampening demand whenFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.126 PART 2 PriceSpikes, Reliability, and Investment5. Regulation has not set K high enough to provide perfect reliability, but that is a different point and thefocus of later chapters.6. To include reserve operating margins in this analysis, it would be necessary to specify a demand curvefor operating reserves. This is discussed in subsequent chapters.7. If the market price were not constant during times when all operable capacity is in use, the right sideof this equation would be the average market price during these times.Figure 2-2.4The load-duration curveflattened by high priceswhen load is limited.power was scarce.5 Consequently, peak demand is higher than is socially optimal.If the costs of peak usage were paid for entirely by the users of peak power,consumers would consume less on peak. Because regulators use average-costpricing, customers pay more at all other times and more in total than they wouldpay if given the relevant choices.The Optimal SolutionThe optimal solution is the same as the regulatory solution except that it takes intoaccount the high cost of serving peak load and the willingness to pay for this service.The optimal system will spend some time with load exactly equal to generationcapacity.6The duration of the flat load peak will be denoted by DPS because at these timesthere is a price spike with price greater than the variable cost of a peaker. If anothermegawatt of peak capacity were added it would produce power for only a fraction,DPS, of the year. The average cost of this energy, ACE, including the fixed cost ofcapacity used to produce it isAverage cost of peak energy =ACE=($6'DPS+$30)/MWh.(See Equation 1-3.2.) Note that this is not the average cost per MW of using peakcapacity, which is plotted in a screening curve, but the average cost per MWh ofenergy produced. The shift in approach is necessary because a consumers valueis given in $/MWh of energy consumed. It only makes sense to add a megawattof peaker capacity if the energy it produces costs no more than its value to consum-ers. According to the assumed demand curve, the value of power to consumersis $1,000/MWh, so the condition for optimal peaker capacity is6'DPS+30 =1000.7February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-2 PriceSpikes Recover Fixed Costs 127Figure 2-2.5The aggregate price spikeof a typicalprice-duration curve.This equation can be solved to find that DPS equals 6'970, or 0.62% of a year, or54 hours per year. If a peaker is needed less than 54 hours per year, it is not worthbuying. Because the load-duration curve is linear, a duration of 0.62 correspondsto a load that is just 25 MW below the potential peak of 8000 MW. The flat peakis at 7975 MW. Total generating capacity should equal this peak load. Althoughconsumers would be willing to pay up to $1,000/MW hour to avoid the curtailmentsimplied by this shortage of capacity, this would not cover the (mainly fixed) costof providing the extra capacity. Because baseload capacity has already beendetermined to be optimal at 6000 MW, the optimal peaker capacity is 1975 MW.The (Aggregate) Price SpikeFinding the competitive solution requires using the long-run equilibrium conditionthat says prices will be at the level that just covers fixed costs. Whether the priceis too high or too low cannot be determined from the average price because thewidth and height of price spikes matter. The individual price spikes are mostconveniently summarized by the price-duration curve (Figure 2-2.5), which isconstructed in the same way as a load-duration curve (Section 1-4.1) but by usinghourly prices instead of hourly loads. As before, duration is measured as a fractionbetween zero and one which can be interpreted as the probability of finding a priceat or above a certain level.A generator recovers fixed cost only when price is above its variable cost. Allsuch prices during the year are summarized by the part of the price duration curveabove this cost. The higher the price, the more fixed cost is recovered, so the areaunder the price duration curve and above the variable cost line gives the averagerate of fixed cost recovery for the year. For example, if the peak of theprice-duration curve were $1,050/MWh, and it dropped linearly to a generatorsvariable cost of $50/MWh at a duration of 5%, its average fixed cost recovery forthe year would be $1,0000.05'2 =$25/MWh, a generous sum.Peakers are often used as a litmus test for whether a market is providing suffi-cient short-run profit to induce investment, but this is not necessary. Any commer-cially viable generation type would serve equally well when the market is inequilibrium, but this book will follow the convention as it causes no harm. TheFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.128 PART 2 PriceSpikes, Reliability, and Investmentpart of the price-duration curve above the variable cost of a peaker will be termedthe aggregate price spike and is often shortened to the price spike. In 1999, PJMestimated this revenue to be approximately $60,000/MWy or $6.85/MWh, and,in 2000, estimated it at $3.40/MWh (PJ M 2001, 1314).

Definitions The (Aggregate) Price SpikeThe (aggregate) price spike is the section of the markets price-duration curveabove the average variable cost of the most expensive-to-run, but still investment-worthy, peak-load generator.The Price-Spike Revenue (Rspike)The area of the price spike is the price-spike revenue. It is the average hourlyscarcity rent that would be earned by the most expensive investment-worthypeaker during the year in question. It can be measured in $/MWh.The Competitive SolutionDetermining what generation capacities would be induced by a perfectly competitivemarket requires the use of Result 2-2.1. Fixed costs are exactly covered in a long-runcompetitive equilibrium. This means short-run profits (scarcity rents) must exactlyequal fixed costs. The trick is to find the short-run profits because fixed costs areknown from Table 2-2.1.As shown in Figure 2-2.3, demand can fall into three different regions classifiedby which plants are marginal. As Figure 2-2.6 shows, if base-load is marginal themarket price is $18; if peakers are marginal the price is $30/MWh, and if themarginal unit of load cannot be served, the price rises to the cap at $1,000/MWh.Figure 2-2.6 shows the price-duration curve for this model. The price spike is theshaded area above $30/MWh, and this provides scarcity rent for both generators.It is the only scarcity rent earned by peakers, so their equilibrium condition is: thefixed cost of a peaker equals the price-spike revenue, Rspike.Baseload plants have two sources of scarcity rent, the price spike and the shadedrectangle between $18 and $30/MWh, which has a duration of Dpeaker, the durationof time when peakers are running. This observation provides the equilibriumcondition for base-load plants, which is given in the Result 2-2.2.

Result 2-2.2 Long-Run Equilibrium Conditions for Two TechnologiesIn the long run, peakers and baseload plants must cover their fixed costs fromshort-run profits (inframarginal or scarcity rents). This implies two equilibriumconditions:FCpeak=RspikeFCbase=FCpeak+(VCpeak!! VCbase) D*peakerThe peakers equilibrium condition implies$6 =$970D*PS,February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-2 PriceSpikes Recover Fixed Costs 129Figure 2-2.6The price-duration curveof the two-technologyexample.The Weak Fixed-Cost Fallacywhere DPS is the duration during which the price is at the cap. The base-loadequilibrium condition implies$12 =$6+$(30!! 18) D*peakerThese two equilibrium conditions can be solved for the optimal durations and, which completely determine the price duration curve and can be used withD*peakerthe load-duration curve to determine the equilibriumcapacities of the two technolo-gies. The solution is DPS=0.62%, Dpeaker=50%, base-load capacity =6 GW, andpeaker capacity =1975 MW. These are exactly the values found for the optimalsolution. Consequently, a competitive market induces exactly the optimal levelsof capacity for both technologies.

Result 2-2.3 Marginal-Cost Prices Induce the Optimal Mix of TechnologiesShort-run competitive prices, which equal marginal costs, provide incentives forinvestment in generation technology, which lead to an optimal level and anoptimal mix of generation technologies.2-2.3 THE LUMPINESS OF FIXED COSTSPoorly behaved costs can interfere with the competitive process and invalidate theEfficient-Competition Result (Section 1-5.1). Natural monopoly conditions,discussed in Section 1-1.1, were the first example. This condition is sometimesconfused with the existence of fixed costs because these cause the average produc-tion cost of a given generator to decline as average output increases. If an industrysFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.130 PART 2 PriceSpikes, Reliability, and Investment8. The effect is small because the total cost function is a smooth function of the number of base-loadgenerators. Near its minimumvalue, it is essentially flat and a deviation fromthe optimal generation setproduces only a second-order effect on cost.average cost declines as total output increases, it is a natural monopoly. A genera-tors average cost always declines until its output nearly reaches its capacity limit.As long as efficiently sized generators have capacities much smaller than the sizeof the industry, their individual declining costs will not cause the natural-monopolycondition.The lumpiness problem. The consideration of natural monopoly leads tothe question of how small the efficient-sized generator would need to be relativeto the size of the market to avoid a problem of inefficiency. For a true naturalmonopoly, one supplier must be able to produce the industrys efficient level ofoutput more cheaply than two or more suppliers. But what if three can produceit more cheaply than two but cannot stay in business with competitive prices becausethey cannot cover fixed costs? This is sometimes called the integer problembecauseit would disappear if fractional suppliers were possible. Sometimes it is called alumpiness problem because supply comes in discrete lumps which may not matchthe level of demand.Suppose generators could be built only with a capacity of 1000 MW and thatdemand had an inelastic peak at a level of 2200 MW. Three plants would be neededto satisfy demand, and failing to build three would cause costly shortages. Withthree plants, excess capacity would cause the competitive price to equal variablecost and all generators would fail to cover their fixed costs. This would lead to aduopoly not because two plants are cheaper, but because competitive prices failto cover fixed costs for the optimal number of plantsthree.This impact of lumpiness is dramatic, but it occurs in an unrealistically smallmarket. Typical markets have at least 100 generators, and most markets in theUnited States have thousands, including those that can participate via interconnec-tions. To gain a more realistic view of the problem, consider the example of Section2-2.2, with the added stipulation that base-load plants always have a capacity of1000 MW while peakers always have a capacity of 100 MW. That market will havehad a peak demand of 7975 MW of which 6000 should be served by six baseloadplants and 1975 should (ideally) be served by 19.75 peakers.Lumpiness of base-load plants. First consider the unlikely possibility thatlumpiness problems caused one too many base-load plants to be built. The seventhbase-load plant would serve a load slice with an average duration of 43.75% ata cost of1000 MW($12/MWh + 0.4375$18/MWh)which comes to $19,875/h. Serving this same load with peakers would cost only1000 MW($6/MWh + 0.4375$30/MWh)This comes to $19,125/h. The extra cost of $750/h is less than 0.4% of the totalcost of serving the market (approximately $200,000/h).8 Inefficiency fromthis typeof lumpiness declines in proportion to the square of the number of generators inFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-2 PriceSpikes Recover Fixed Costs 1319. This cannot be seen froma deterministic analysis, but with the uncertainties of real markets and thedifficulties of coordination between competitors, it is impossible to maintain an excess-profit equilibrium.the market. For a real market with hundreds of generators, the inefficiency wouldbe many times smaller.Lumpiness of peak-load plants. A realistic analysis of the peaker situationwill need to take account of the randomness in real markets. Building 19 peakerswould result in supply being short of demand for a duration 4 times greater thanis optimal (2.5% instead of 0.62%), and this would cause peakers to over-recoverfixed costs by a factor of four. These high profits would entice the entry of anotherpeaker which would drop short-run profits to zero. This would stop entry as demandgrew. With free entry and the uncertainties of a real market, short-run profits wouldaverage out to the level of fixed costs.9 But lumpiness would prevent the right(fractional) number for peakers from being built, and this would cause someinefficiency.Given the integer constraint, 20 peakers should be built, but for short-run profitsto equal fixed cost, there must be only 19 peakers in the market 25% of the time.With only 19 peakers, some load will be unserved, relative to variable cost, fora duration of 2.5%, and the amount unserved will average 50 MW. At the valueof $1,000/MWh indicated by the demand function, the average value of unservedload comes toValue of unserved load =$(0.025501000)/hwhich is $1250/h. This loss is offset by the savings of not building the peaker, whichis $600/h and the saving of not producing for the load peak, which is only $37.50/h.The net loss is about $600/h, but this occurs only for the 25% of the time whencapacity is under-built. The average loss from the lumpiness of peakers is about$150/MWh or less than 1'10 of 1% of the total cost of power.

Result 2-2.4 Inefficiency Caused by the Lumpiness of Generators Is NegligibleIn a power market with more that 4 GW of peak load and a 400 MW connectionto a larger market, inefficiency caused by the lumpiness of the generators is wellbelow 1% of retail costs. This inefficiency declines in proportion to the size of themarket.A realistic assessment of lumpiness. The base-load calculation overestimatedthe lumpiness problem by assuming that the market would always build the wrongnumber of base-load plants. The peaker calculation overestimated by assumingthat load duration is far more sensitive to total generating capacity than is realistic.(Real load-duration curves have a narrow spike, not a shallow linear slope.) Manyother factors enter the picture and, in general, the more flexibility that is added inother dimensions, such as demand elasticity or the availability of smaller plants,the smaller the problem becomes.A more intuitive approach is to ask how much would be gained if fractionalplants could be built. If the Eastern Interconnection could add 0.75 more peakersinstead of either zero or one, would this allow a finer tuning of installed capacityFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.132 PART 2 PriceSpikes, Reliability, and Investmentand a more efficient market? No one believes that optimal capacity can be estimatedwith even 1'100 of this precision. Transmission constraints may exacerbate theproblem a bit, but the flexibility to build fractional plants would make a detectabledifference only in the smallest markets. In conclusion, competitive prices would cover fixed costs and induce the optimalmix of generation technologies with a great deal of precision. The problems ofpower markets do not arise from fixed costs but from the difficulty in achievingcompetitive prices in the face of demand-side flaws.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. Both distribution and transmission outages typically cause more loss of load.Edison's design was a brilliant adaptation of thesimpleelectrical circuit: theelectric companysends electricity through a wireto a customer, then immediately gets theelectricity back throughanother wire, then (this is thebrilliant part) sends it right back to thecustomer again. Dave BarryChapter 2-3Reliability and GenerationRELIABILITY IS AT THE HEART OF EVERY DEBATE ABOUT ENERGYPRICE SPIKES. If these are large enough, they induce the investment that providesthe generating capacity necessary for a reliable system. In some markets capacityrequirements also play an important role. A shortage of installed generating capacityis not the only cause of unreliable operation, but because it is the one most directlyrelated to the operation of the wholesale markets, it is the only one considered inPart 2.1Two aspects of reliability are always contrasted. Security is the systems abilityto withstand sudden disturbances, while adequacy is the property of having enoughcapacity to remain secure almost all of the time. Part 2 focuses on adequacy andassumes that security requirements will be met if the system has adequate planningreserves. Requirements for operating reserves, which are intended to providesecurity, are of interest here mostly because of their role in raising price, stimulatinginvestment, and thereby contributing to adequacy. This role is often overlookedbecause, under regulation, these requirements were unrelated to adequacy.Chapter Summary 2-3: Operating reserves can be purchased directly by thesystem operator, but the market must be induced to provide adequate planningreserves. The first step in analyzing the markets effectiveness is to find whatdetermines the optimal level of installed capacity. Under a simple but useful modelof reliability, installed capacity is found to be optimal when the duration of loadshedding is given by the fixed cost of a peaker divided by the value of lost load.Section 1: Operating Reserves and Contingencies. A contingency is apossible or actual breakdown of some physical component of the power system.Typically, some operating generator becomes unavailable, leaving the systemFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.134 PART 2 PriceSpikes, Reliability, and Investmentunbalanced with demand greater than supply. System frequency and voltage beginto drop. If sufficient operating reserves are available so lost power can be replacedwithin 5 to 10 minutes, the system operator will usually not need to shed load.Section 2: Adequacy and Security. Reliability has two components. Adequacyis a matter of installed generating capacity and does not fluctuate from minute tominute. Security refers to the systems ability to withstand contingencies, and systemsecurity can change from minute to minute. Immediately after a contingency, andbefore operating reserves have been replenished, the system is much less secure.Though security depends on generation and transmission, only generation will beconsidered. A power system has adequate generation if it has enough to keep itsecure in all but the most extraordinary circumstances. Section 3: The Simple Model of Reliability. Out-of-service generation maybe thought of as a load on the system and added to actual load. If this augmentedload is greater than installed capacity (Lg>K), then load must be shed. Other times,load is shed for reasons unrelated to K. The simple model assumes that, except forthese unrelated reasons, loss of load is exactly Lg!! K or zero when this is negative.Lost load is assumed to cost customers a constant amount per MWh lost. Withthis additional assumption, the optimal amount of installed capacity is the amountthat makes the duration of load shedding equal to the fixed cost of a peaker dividedby VLL.Section 4: The Fundamental Reliability Question. The amount of lost loadmight be greater than the difference between Lg and K. For instance, cascadingfailures might be triggered by a high value of Lg!! K, and these cause much morethan Lg!! K to be shed. The extent of the discrepancy between the Simple Modelof Reliability and reality is an engineering question that deserves attention.2-3.1 OPERATING RESERVES AND CONTINGENCIESPower systems experience frequent disturbances such as short circuits or loss ofgenerators or transmission lines. The possibilities of such events are called contin-gencies, and often the term is misapplied to the events themselves. Such eventsreduce the amount of generation available to serve load, and for present purposesit will be sufficient to imagine a disturbance as a generator experiencing a forcedoutage.When this happens, frequency and voltage immediately begin to drop. If theydrop too far for too long, load must be shed to rebalance demand with the dimin-ished supply. In the first instant after a forced outage all remaining generatorsincrease their outputs with the extra power coming from the kinetic energy of theirrotation, not from their fuel source. As this energy is depleted, they slow down andthe system frequency drops as does the voltage. These changes cause loads to drawFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-3 Reliability and Generation 1352. For an economically informed discussion of reliability, see Felder (2001).less power, and the system comes into balance at a lower frequency. This takesonly a matter of seconds. The decline in system frequency is immediately detectedby frequency censors, and the ones with excess capacity (those that provide regula-tion and spinning reserve) begin to ramp up.If there are not enough spinning reserve generators to ramp up and restore systemfrequency in the required 5 to 10 minutes, then the system operator is required toshed load. Thus spinning reserve and load shedding are substitutes for the serviceof restoring system frequency. (Shedding load will always mean the involuntarydisconnection of load.) Just how perfectly load-shedding can substitute for reservesis considered in Section 2-3.4.Operating reserves include spinning reserves and several lower qualities ofreserves. Typically, 10-minute spinning reserves are the first defense against acontingency. They are supplied by generators operating at less than full capacity.Because they are already synchronized with the AC system(spinning), they respondwithout delay, but their response is gradual. They can typically ramp up at someconstant rate, such as 4 MW per minute. In this case they are given credit forsupplying 40 MW of 10-minute spinning reserve because they can increase theiroutput by that amount in 10 minutes. Other types of operating reserves are10-minute and 30-minute nonspinning reserves. Generators that are off line butcan be started quickly can supply nonspinning reserves.2-3.2 ADEQUACY AND SECURITYOperating reserves are required to maintain system security by handlingshort-term disturbances to the system. Planning reserves are required to maintainsystem adequacy by meeting annual demand peaks. These two types of reserveare considered the basic inputs to the generation side of system reliability. (Thetransmission side of reliability is not considered in Part 2). Although security andadequacy are distinct concepts, they are closely linked. A system with adequatecapacity can maintain enough security to reduce periods of involuntary loadshedding to 1 day in 10 years. A system that maintains security for all but one dayin 10 years must have adequate installed capacity.2

Definitions SecurityThe ability of the electric system to withstand sudden disturbances such aselectric short circuits or unanticipated loss of system elements (NERC,1996).AdequacyThe ability of the electric system to supply the aggregate electrical demand andenergy requirements of the customers at all times, taking into account scheduledand reasonably expected unscheduled outages of system elements (NERC,1996).The two concepts are not simply different views of the same problem. Withan inappropriate policy on operating reserves, the system will have insufficientFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.136 PART 2 PriceSpikes, Reliability, and Investment3. This assumes an isolated system. Two neighboring systems, competing for each others operatingreserves, will bid prices up and make their procurement expensive.security in spite of adequate capacity. Nonetheless, it is relatively cheap to maintainsufficient operating reserves in an adequate system, and it is relatively expensiveto provide for system adequacy.3 Adequacy is the crucial economic problem, whilethe problem of security is economically secondary yet complex.To focus on the problems of investment in generation and system adequacy,Part 2 assumes that the operating reserve policy is always effective in providingas much security as possible (up to the normal standard) given the systems installedcapacity. There are many such policies, but all must provide a certain minimumlevel of reserves. The Simple Model of Reliability, described in the next section,assumes that load will never be shed unless it exceeds the amount of operablegeneration capacity. Section 2-3.4 considers possible exceptions to this assumption.2-3.3 THE SIMPLE MODEL OF RELIABILITYPart 2 will rely on the Simple Model of Reliability which assumes a well-definedlevel of installed generation capacity, K, and generation outages, g, both measuredin megawatts. Load, L, is defined as the economic demand for power, the amountof power that would be consumed if the system were operating normally. Becauseoperating reserves are assumed to be available whenever needed within the limitsof installed capacity (K), it does no harm to define them to be all installed capacitythat is neither out of service nor serving load. Thus,Operating reserves =OR =K !! g !! LBecause load is defined here to be economic demand (see Section 1-4.3), it canexceed supply. In this case there is lost load, LL, and there is served load, and thesum of the two is load, L. Lost load is measured by the extent to which OR isnegative, and is zero whenever OR is positive; thus,Lost load =LL =max( !!OR, 0)In reality, load may be shed even when OR >0, and when OR is negative, morethan LL may be shed. Such excess service interruptions include those caused bydistribution faults and cascading outages. The simple model assumes that excessinterruptions are not correlated with the level of operating reserves. If they are notcorrelated, they are not affected by increasing K, and are a constant cost which canand will be ignored. Thus LL does not include all lost load, but within the simplemodel it includes all that can be affected by a policy that controls installed capacity,K. The lack of correlation between excess loss of load and OR is the key assumptionof the Simple Model of Reliability and is discussed further in Section 2-3.4. Withthis assumption, nominal lost load, LL, is easily computed and is all that matters.Defining augmented load, Lg, as L +g, simplifies the definition of OR to . K !! LgOperating reserves are just installed capacity less augmented load. Taking a genera-tor off the system is electrically equivalent to placing an equal load on line at theFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-3 Reliability and Generation 1374. Because unplanned generation outages cause an increase in Lg when they occur unexpectedly, theycorrelate with Lg. Because planned outages are scheduled at times of the year when L is low, they have asecond broad peak for low values of Lg.Figure 2-3.1The Simple Model ofReliability.generators point of connection. Thus, a generators outage is equivalent to an equalincrease in load at its point of connection.

Assumption 2-3.1 Load is Shed Only to the Extent Necessary: LL =max(Lg!! K, 0)Systematic (nominal) lost load (LL) equals the amount by which augmented load,Lg, exceeds installed capacity, K. Augmented load includes economic demand,L, and generation out of service, g. Systematic refers to losses that are corre-lated with . Lg!! KFigure 2-3.1 shows how load is lost when augmented load exceeds K, typicallybecause of an unexpected forced outage. There are also planned outages formaintenance. Although outages contribute to augmented load, they cannot be lost;only real load can be shed when augmented load exceeds capacity. To account forthis, g should be considered to contribute to the bottom of Lg rather than to the top.Augmented load, just as real load, can be represented by a load-duration curveas depicted in Figure 2-3.2. Generation outages are shown at the bottom to indicatethat they cannot be part of lost load, but they are shown with a dotted line becausethey are not represented by a load-duration curve; instead, their correlation withLg is depicted.4 The peak of Lg is above K, and this causes load shedding. The areaof the region labeled LL gives the expected annual average load shedding, LL

, inMW, while DLS is the duration of load shedding and has a typical value of 0.03%(.0003) corresponding to 1 day in 10 years.The Fundamental Reliability ResultFigure 2-3.2 shows that given well-functioning security procedures, generationadequacy (represented by installed capacity, K) is the fundamental determinantof reliability. The greater is K, the smaller is the area of lost load. Increasing Kreduces the cost of lost load but increases the cost of serving load. This costtrade-off determines the optimal value of K.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.138 PART 2 PriceSpikes, Reliability, and InvestmentFigure 2-3.2An augmented-load-duration curve.Lost load, LL, fluctuates from minute to minute and cannot be used directlyto compute the necessary amount of installed capacity which can change only veryslowly. Instead, an average value of LL is needed. The cost of both instantaneouslost load, LL, and average lost load, LL

, can be found by multiplying these megawatt

values by the value of lost load, VLL, measured in $/MWh. The resulting cost ismeasured in dollars per hour ($/h). Increasing K by 1 MW would reduce the areaLL

by DLS MW where DLS is the duration for which the augmented load is morethan K. This would reduce the average cost of lost load by $(VLLDLS)/h.From Equation 1-3.1, the average cost of adding (peaker) capacity is given byDLSVCpeak. Because DLS is so small (0.0003), the fixed-cost term domi- FCpeak+nates. Most of the cost of serving peak load is the fixed cost of purchasing thepeaker, so the role of DLS in determining the cost of adding 1 MW of peak capacitycan be ignored.As K increases DPS decreases. For low values of K, VLL DLS will be greaterthan FCpeak, and it will cost less to increase K than will be saved by the reductionin lost load. For high values of K the reverse is true, and at the optimal K, the costsaved equals the cost of installing another megawatt of peak capacity. The conditionfor optimal K isVLLDLS=FCpeakPolicy can control neither VLL nor FCpeak, so it must control DLS. The optimal valueof DLS is given by D*LS=FCpeak'VLL A reliability policy that induces investment when, and only when, DLS<FCpeak'VLLwill be optimal, at least according to the Simple Model of Reliability.Result 2-3.1 is important because it characterizes the optimal equilibrium basedon very little information. It is true regardless of the probability distribution ofgeneration outages or the shape of the load-duration curve or the shape of dailyload fluctuations.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-3 Reliability and Generation 139

Result 2-3.1 Optimal Duration of Load Shedding Is D*LS=FCpeak'VLLIn a power system that satisfies Assumption 2-3.1, the optimal average annualduration of load shedding, D*LS, is equal to FCpeak'VLL, where FCpeak is the fixedcost of a peaker and VLL is the cost per MWh of lost load (VOLL). Only loadshedding that is affected by K is included in D*LS.2-3.4 THE FUNDAMENTAL RELIABILITY QUESTIONAssumption 2-3.1 leads to load-shedding Result 2-3.1, which gives a fundamentalcharacterization of the optimally reliable power system. This characterization statesthat the optimal duration of nominal load-shedding is given by FCpeak'VLL, whichis independent of all system characteristics except the two named costs. Nominalload shedding, LL, was defined to be Lg!! K when the difference is positive.This is a claim that markets may put to the test. For example, under regulation,the energy price does nothing to limit peak demand so the load-duration curve underregulation is often sharply peaked. This means a system with five hours of loadshedding might have only 30 hours with spinning reserves under 4%. But a marketwill dramatically flatten the peak of the load-duration curve by raising pricewhenever reserves are low. In this case, a system with five hours of load sheddingmight have 300 hours with spinning reserves below 4%.It seems possible that the market system might have significantly less reliabilityeven though it had the same value of LL. In particular, it might be more susceptibleto cascading failures as the result of spending more time with low reserve (e.g.,less than 4%) or because of more short-duration load-shedding incidents.Another possibility is that the control of load-shedding is not precise enough,either with regard to the amount of load shed or how quickly it can be shed. In thiscase load shedding may be greater than Lg!! K simply because it cannot be con-trolled accurately. The technology for such control, however, would seem to bereadily available and inexpensive. If so, any discrepancy between Assumption 2-3.1and reality may be quickly overcome.This discussion should not be read as an argument for or against Assumption2-3.1. The point is simply that the question of its validity deserves more attentionand can be evaluated from a purely engineering perspective.

Question The Fundamental Reliability QuestionDoes Assumption 2-3.1 hold, with reasonable accuracy, in actual power systems?If this assumption is far wrong, then VOLL pricing as well as several of its lesshigh-priced relatives are wrong in theory, quite possibly by a significant amount.As long as load-duration curves remain close to their familiar shapes, this willprobably cause little trouble. But once increased demand elasticity moves theminto unfamiliar territory, a better understanding of reliability may become essential.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Wedont know what thehell it is, but its very largeand it has a purpose. Dr. Heywood Floyd2001, A Space Odyssey1968Chapter 2-4Limiting the Price SpikesWHEN SUPPLY CANNOT EQUAL DEMAND, THE MARKET CANNOTDETERMINE A PRICE. When contemporary power markets have enough installedgeneration capacity (ICap) to prevent this market failure at all times, they have somuch that generators cannot cover their costs. This contradiction occurs only forcertain combinations of supply, demand curves and load-duration curves, but whenit does occur, the market fails; there is no long-run equilibrium. Most current powermarkets may well satisfy the conditions for this failure.The demand-side flaws are the cause of this market failure, but they need notbe eliminated in order to remove it. Failure can be prevented simply by reducingthe severity of the first demand-side flawby increasing demand elasticity. Untilthis is accomplished, the systemoperator must set the market price when the marketfails to clear. At these times, some regulatory rule must be adopted for determiningwhat price to set. If price is set only for these few hours, it must be set extremelyhigh, so it may be better to set price more often and lower. Such details are consid-ered in subsequent chapters. The purpose of this chapter is to explain why all currentpower markets need and have price limits.FERC approved price limits of $750, $500 and $250/MWh for Californiabetween 1998 and August 2001. In the summer of 2000 it reduced the NY ISOslimit from its previously approved level of $10,000 to $1,000/MWh bringing itin line with PJ Ms limit. A year later it limited prices indirectly in the West toroughly $100/MWh. In between it suggested that what Western markets reallyneeded was no price limit at all. The Australians tell us prices must be capped atthe value of lost load, which they put at between $15,000 and $25,000/MWh AU.The new electricity trading arrangement in England allows much higher prices andpromptly set a record of over $50,000/MWh. Settling on a reasonable policy willrequire understanding the nature of failure in power markets.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-4 Limiting thePriceSpikes 141Why Power Markets Fail(and What Caps Their Price)Three conditions are necessary for failure: (1)inelastic demand, (2) inelastic supply, and (3)volatile demand. Given the proper realization ofthese conditions, imagine starting with too muchgenerating capacity. As capacity decreases towardan equilibrium level, short-run profit will increase, butbefore it becomes great enough to cover fixed costs,the supply and demand curve will fail to intersect.This is market failure. Price is pushed toward infinity,but even an infinite price cannot clear the market.Current power markets probably satisfy the condi-tions required for this failure, which is why they haveprice caps.A less extreme form of the failure may occur. Theclearing price may rise above VLL (the average costto customers of load being shed) before short-runprofit covers fixed costs. In this case there may be along-run equilibrium but it would be less efficientthan one that caps price at VLL and sheds load.With the first failure, the system operator must setprice because the market cannot; with the second itshould set price because the market sets it at morethan power is worth. Because of the seconddemand-side flaw (Section 1-1.5) no customer willpay more than the highest price the system operatorpays for power. So the limit on the system operatorsprice limit caps the price in all energy markets. Thisoccurs through arbitrage and without any regulatoryrestrictions except the limit on how high a price thesystem operator should pay.Chapter Summary 2-4: Most, if not all, contemporary power markets wouldfail to have a long-run equilibrium were it not for the regulatory setting of real-timeprices by the system operator. This price setting is needed only when the marketfails to clear and sets no price of its own, or when it sets a price greater than thevalue of power to customers. The system operator must purchase power on behalfof loads and should set a price no higher than the average value of power toconsumers. The second demand-side flaw, one of the two causes of the marketfailure, makes it impossible for customers to buy more-reliable power in advancethan they can in real time. Consequently, the system operators price limit capsthe entire power market.Section 1: Normal Market Operation with Lim-ited Demand Elasticity. In spite of the demand-side flaws, contemporary power markets could operatenormally and efficiently with a modest amount ofdemand elasticity, provided the load-duration curvedoes not have too sharp a peak. In this case no regula-tory price intervention would be needed or desirable.Section 2: Market Failure with a Steep Load-Duration Curve. By replacing the rather flat peakof the load-duration curve of Example 1 with onehaving a more realistic and sharper peak, Example 2illustrates the possibility of market failure. In thisexample, the market has no long-run equilibrium un-less the system operator sets a price in the real-timemarket whenever the supply and demand curves donot intersect and load must be shed.Section 3: Suppressing the Balancing Marketto Avoid Regulating Price. Some suggest suppress-ing the systemoperators balancing market so the pricewill not need to be regulated. The only practical ap-proach is to set the price in that market high enoughthat the market is not used. This avoids the problemof setting the wrong regulated price by effectivelysetting it so high that all trade is stopped and thenclaiming there was no regulation because there wasno trade.Section 4: Setting Price to the Last Clearing Price. When the systemoperatormust set price, a simple market-based rule is desired. To this end, setting price toFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.142 PART 2 PriceSpikes, Reliability, and Investment1. Borenstein (2001a) identifies the fundamental problemwith electricity markets [is that] demand isalmost completely insensitive to price fluctuations and supply faces binding constraints at peak time. andpredicts short-termprices for electricity are going to be extremely volatile. Green (1998) observes Ifcustomers cannot react in this way [to price], and random power cuts are needed, then there is no limitto the price that the generators could set, if they were allowed to set it after the shortage has appeared.the highest demand bid, or more generally to the last market-clearing price, hasbeen suggested. Either rule can produce a price that is too high or too low becauseneither rule relies on relevant information. Such rules can be less efficient thansimply building so much generation that price never rises above the marginal costof a peaker.Section 5: Real-Time Price Setting Caps the Forward Markets. The highestprice that the system operator will pay when it must set a price is termed Pcap, andthis limit should be no higher than the value of lost load. Because the systemoperator must break even on its trades, it will charge no more than Pcap for real-timesales. Because of the second demand-side flaw, there can be no advantage to buyingpower in advance. As a consequence, the system operators limit, Pcap, will limitthe price of power in all real-time and forward markets, both public and private.Section 6: Technical Supplement: The Condition for Failure. This sectiongives the technical condition for the failure of a long-run equilibrium to existwithout regulatory price intervention. It also gives the condition for the equilibriumto be as efficient as possible, given the first demand-side flaw, when an equilibriumexists and price is not regulated.2-4.1 NORMAL MARKET OPERATION WITH LIMITED DEMAND ELASTICITYChapter 2-2 analyzed a power market which behaved normallyone inwhich the supply and demand curves were bound to intersect. But realpower markets have limited elasticity and so the intersection of supplyand demand is not guaranteed.1Example 1. A slight modification of the model used in Section 2-2.2will make such a failure to intersect possible and will serve as Example 1.The supply side of the model remains unchanged with two types of suppli-ers both of which produce at a constant marginal cost up to their capacitylimit. At this point their marginal cost rapidly climbs to infinity. Their fixedcosts, as in Chapter 2-2.2 are $6 for baseload plants and $12/MWh forpeakers.Maximum demand, demand at a low price, fluctuates uniformly between 4000and 8000MW. One hundred megawatts of that load is willing to curtail at$1,000/MWh, but the remainder has no ability to respond to price. Suppose allunpriced load values its consumption of power at exactly $10,000/Mwh (this doesnot affect the demand curve). The supply and demand curves are shown in Figure2-4.1.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-4 Limiting thePriceSpikes 143Figure 2-4.1Example 1, a flawedmarket with an efficientequilibrium.Using Result 2-2.2, the equilibrium conditions are found to be 6 =DPS(1000!! 30)and 12 =6 + Dpeaker(30!! 18)Solving these gives DPS=0.62% (or 54 hours/year) and Dpeaker=50%. The loadduration curve (Figure 2-2.4) indicates equilibrium baseload capacity will be 6000MW and optimal peaker capacity will be 1975 MW for a total of 7975 MW. Thisis the same solution as found in Section 2-2.2 because the left part of the demandcurve, which used to be horizontal but is now vertical, plays no role. In the long-runequilibrium, the right-most vertical part of the supply curve is never found to theleft of the 100-MW region of demand elasticity.In this market, even though the supply and demand curves both become verticaland would fail to intersect with a 1% (75'8000) increase in demand on peak, themarket will build enough generation to prevent this. The system operators roleis limited to clearing the market, which is always possible. There is no need to placeany limit on the price the system operator should pay. This market suffers fromneither demand-side flaw although both are present and could be exposed bydifferent circumstances. Price is not regulated, and the market is fully competitiveand efficient.

Result 2-4.1 A Small Amount of Elastic Demand Can Make the Market EfficientEven if demand can be reduced less than 2% by a price increase, this couldproduce a long-run market equilibrium. Such an equilibrium could be moreefficient than any price-regulated version of the market in spite of the presenceof both demand-side flaws.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.144 PART 2 PriceSpikes, Reliability, and Investment2. Two tenths of one percent is the duration corresponding to the maximumprice-response of load, whichis 100 MW. The maximumclearing price is $1,000/MWh, and the variable cost of a peaker is $30/MWh.2-4.2 MARKET FAILURE WITH A STEEP LOAD-DURATION CURVEExample 2. The above example uses a linear load-duration curve, while powermarkets typically have sharply peaked curves. In that example, load spent 2.5%of the time within 100 MW of the peak. Suppose, more realistically, that load onlyspent 0.2% of the time within 100 MW of the peak. Algebraically, the peak regionof this load duration curve and the curve from the previous example can be ex-pressed as follows:Example 1: % Duration =(8000!! load)'40.Example 2: % Duration =(8000!! load)'500.If the market built 7975 MW of capacity, as in Example 1, peakers would earnscarcity rents (positive short-run profits) only about 0.05% of the time for anaverage fixed-cost recovery of roughly $0.50/MWh (0.05% of $1,000/MWh). Thisis far too little, so investment would stop.As installed capacity dwindled, short-run profits would increase. Ifinstalled capacity declined below 7900 MW, there would be times at whichthe supply and demand curves would fail to intersect. The maximumprice-spike revenue that can be generated by this market without the marketfailing during peak-load hours is 0.2%(1000!! 30), or $1.94/MWh.2This is too little to cover the fixed costs of peakers, $6/MWh in theseexamples.With this level of price-spike revenue, neither peakers nor baseloadplants would cover their fixed costs and investment would stop. Plantretirements would decrease supply and load growth would increasedemand with the result that the market would fail to clear for an increasingfraction of the year. This is market failure. When the supply and demandcurves do not intersect the market cannot determine price, and the systemoperator cannot set price to the market-clearing price because there is no such price.This leaves only two possibilities: (1) the system operator can set a regulatedprice whenever demand exceeds supply at every price; or (2) the system operatormight avoid trading at times of peak demand. The first approach admits that thereal-time market has failed and provides a regulatory patch. The second approachadmits it has failed and shuts it down whenever it fails to clear. The hope for thesecond approach is that some substitute will be provided in the forward markets.That possibility is explored next.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-4 Limiting thePriceSpikes 1453. Even if possible, it would be complicated because power injections cannot be physically matched tospecific loads. If two loads have a contract for 100 MW with a particular supplier and are using that muchpower, and the generator is injecting only 150 MW, there is no physical indication of which load is shortof power. The complexity of this problemincreases when loads contract with multiple suppliers.

Result 2-4.2 Too Little Demand Elasticity Can Cause the Real-Time Market to FailEven if demand is sufficiently elastic for the market to produce a long-runequilibrium without the help of regulated prices, it may possess no such equilib-rium if the load-duration curve has too sharp a peak relative to the elasticity ofdemand.2-4.3 SUPPRESSING THE BALANCING MARKET TO AVOID REGULATING PRICENormally the system operator conducts a real-time market, also known as a balanc-ing market, for the purpose of maintaining system frequency, voltage, stability andreliability in general. The previous section demonstrated that the investmentdynamics of some power systems will bring their ICap level into the region ofmarket failure where the system operator is forced to set a real-time price if itcontinues to operate the balancing market. Some suggest that this failure can and should be avoided by effectively shuttingdown the system operators balancing market, at least in times of supply shortage(private real-time bilateral trading would continue). While this suggestion may seemtoo irresponsible to be taken seriously, and Part 3 argues that it is not a practicalapproach to providing reliability, the influence of this suggestion on the designof the new British market, and even within FERC, requires that it be addressed.The market could be shut down either permanently or only when it failed tohave a clearing price. This section answers two questions: (1) Is this practical? (2)Would it be superior to keeping the balancing market open and regulating its pricewhen necessary?The Impracticality of Suppressing the Balancing MarketBesides the difficulty of providing the balancing services required for reliabilitywith only a private, bilateral real-time market (see Part 3), the second demand-sideflaw makes withdrawal of the system operator from the real-time market quitedifficult. The system operator could take either of two approaches when attemptingto remove itself from this market: (1) It could shed load; or (2) it could charge ahigh price for taking power during a shortage.One approach to withdrawing from the market would be to require balancedcontracts and physically curtail any load whose supplier fails to meet a contractualobligation equal to its load. This is physically impossible, however, in contemporarypower systems as noted by the second demand-side flaw.3The First Approach. Consider a time when demand exceeds supply and thesystem operator is attempting to suppress its balancing market by shedding load.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.146 PART 2 PriceSpikes, Reliability, and InvestmentCustomers will be disconnected involuntarily, and this will leave connected loadexactly equal to operating capacity. Only by coincidence would each customerpossesses a forward contract for exactly the amount of load left connected. Thisis true for two reasons: (1) load shedding disregards contracts, and (2) knowingthis, customers have no reason to try to match their contracts exactly to theirexpected load (see Section 2-4.5). As the matching is imperfect, some customers will be oversupplied and someunder-supplied relative to their contracts. The system operator will be taking powerfromsome suppliers whose customers do not need all their power (perhaps becausetheir load was shed) and giving it to other consumers who have contracted for toolittle. Load shedding does not result in balanced bilateral contracts but leaves mostcustomers trading some power with the system operator. This requires the systemoperator to set a price on those trades. The first approach does not accomplish itsobjective.The Second Approach. The second approach charges a high price wheneverdemand exceeds supply. Knowing the price will be high, load will pay a high pricein forward markets to avoid having to buy power from the system operatorsbalancing market when that market is short of supply. The combination of highforward prices and high balancing prices will lead to investment in generation anda reduction in the hours during which the balancing market will fail. Charging avery high price during failures does not result in shutting down the systemoperatorsmarket when that market fails to clear but does reduce the time during which failureoccurs. Sometimes, excessively high prices, unrelated to cost, are termed penaltiesand this approach could be viewed as imposing a severe penalty on trade with thesystem operator during periods of load-shedding.This approach is successful at reducing the period of market failure. With asufficiently high penalty/price that period might be reduced to zero. Then it wouldbe the same as the regulatory price setting approach discussed in the previoussection, but in an extreme form.Is There an Advantage to Suppressing the Market?The first approach is unworkable, the second is equivalent to setting such a highregulated price or such a high penalty that the market shuts down. This preventsthe market failure of Example 2 by regulating the market out of existence.But this market only disappears when load-shedding disappears, because load-shedding unbalances the trades and thus forces trade with the system operator.Forcing an absolute avoidance of load shedding, as will be seen in the followingchapter, is equivalent to using too high a value for VLL in VOLL pricing. This forcesthe market to provide too much reliability.Because power would necessarily be purchased in forward markets, thoughperhaps only day-ahead forward markets, price spikes would necessarily be lowerand of longer duration. This might mitigate the side effects caused by volatility.Perhaps the main drawback to suppressing the centralized real-time market isthe associated loss of efficiency. This is a valuable market because it allows last-February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-4 Limiting thePriceSpikes 147The Reliability FallacyThe Regulatory-Price-Spike Resultminute corrections to be made very efficiently. This is discussed in more detailin Chapter 3-3.

Result 2-4.3 Suppressing the System Operators Balancing Market Is InefficientSuppressing the system operators balancing market is equivalent to setting theregulated price in that market extremely highhigh enough to induce so muchgenerating capacity that load would never be shed. This prevents the marketfailure by regulating the market out of existence. It is inefficient to induceabsolute reliability, and the loss of the centralized real-time market also reducesefficiency.Conclusion to Example 2. Result 2-4.3 shows there is no way to avoid themarket failure of Example 2. If the system operator does not intervene, installedcapacity will decline below its optimal value and continue to fall until supply failsto intersect demand for some part of the year. Even at this level it would continueto fall if the system operator did not intervene. The only two possible interventionsare to set a price or shut down the real-time balancing market. Result 2-4.3 showsthe latter to be inefficient. This leaves setting a price as the only method of provid-ing an efficient level of reliability. As long as the first demand-side flaw is suffi-ciently severe, the market cannot solve the reliability problem on its own.F FF Fallacy allacy allacy allacy 2-4.1 The Market Will Provide Adequate ReliabilityContemporary markets, even with their demand-side flaws and negligible demandelasticity, could still provide reasonable investment incentives and a reasonablelevel of reliability if regulators and engineers would refrain from setting orlimiting prices.Given the market flaws, the system operator must set the price whenever supplyfails to intersect demand. In present markets this will mean setting price most ofthe time it is above the left-hand marginal cost of the most expensive generator.Thus the entire aggregate price spike will be determined by regulator policy. Aswill be seen in subsequent chapters, there is considerable choice as to how highthe price spike will be and how long it will last, but the conclusion at this pointis simply that it must be determined by the system operator if an efficient level ofreliability is to be achieved.Result 2-4.4 Regulatory Policy Determines the Height and Duration of Price SpikesBecause of the second demand-side flaw, markets will not set energy priceshigher than the system operators price limit. Consequently this regulatory limitdetermines the height of price spikes. The average annual duration of spikes iscontrolled by the application of this limit to the operating reserve requirement.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.148 PART 2 PriceSpikes, Reliability, and InvestmentPeak DurationsThree durations related to peak load have been used.DLSDuration of load shedding: Lg>KDPSDuration of the price spike: Lg>K ! ! ORRDpeakerDuration of peaker use: Lg>Kbase! ! ORRChapter 2-2 considered a market in which demandonly became elastic at $1,000/MWh, so DLS=0.Under VOLL pricing, DLS=DPS. In other cases:DLS<DPS<Dpeaker.2-4.4 SETTING PRICE TO THE LAST CLEARING PRICEExample 2 demonstrated that some markets cannot sustain sufficient installedcapacity (ICap) to prevent market failure. In these markets, as long as marketclearing is assured, there is so much ICap that prices and short-run profits are toolow to cover the fixed costs of the installed generation. Retirement of older plantsand load growth will ensure that, in equilibrium, ICap is low enough that for somefraction of the time demand will exceed supply at any price. During these timesthe system operator is forced to set a regulated price, which, if properly selected,will be high enough to cover the fixed costs of the optimal quantity of ICap.While setting an optimal price is desirable, so is lack of regulatory interferencewith the market. Although the system operator must set some price, perhaps it couldset one related to the market in some natural and transparent way. One candidatefor this was proposed for ERCOT, the Texas ISO. Its rule is to let the highestdemand bid set the price after the market fails to clear as well as just before it failsto clear. In the present example, this would mean leaving the price at $1,000/MWhafter demand exceeded supply.This price-setting rule can be generalized to require the system operator to keepthe price at the last market-clearing price after the market fails to clear, regardlessof whether that price was set by a supply bid or a demand bid. In the presentexample this change would make no difference.Example 3: Analysis of a $1,000/MW Price LimitInstructing the system operator to use the lastmarket-clearing price once demand exceeds supplywill mean keeping the price at $1,000/MWh in thepresent example. This will define Example 3 whichdiffers from Example 2 only in that the systemopera-tor provides this regulated price whenever the marketfails to clear. No regulator intervention was madein Example 2. As determined in Section 2-4.1, theprice must stay at this level for a duration of 0.62%in order to cover the fixed costs of generators. InExample 1, this equilibriumwas optimal because thecurtailment of load was voluntary and based onprice. This was a standard competitive equilibriumwith the supply curve always intersecting the demand curve. In Example 3, if ICap is 7691 MW, load will exceed it for a duration of 0.62%.As shown in Figure 2-4.2, this will force load to be reduced by 309 MW on peakthrough a combination of 100 MW of demand elasticity and 209 MW of loadshedding. As a simple check on the efficiency of this equilibrium consider the costof load shedding. With a value of lost load of $10,000/MWh, load shedding canbe computed to cost an average of $4,380/h (every hour, not just during peakhours). With a fixed cost of $6.00/MWh, 309 MW of peaking capacity would costFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-4 Limiting thePriceSpikes 1494. All values in these examples have been rounded. The exact values and detailed calculations can befound at www.stoft.com. Calculations for Example 3 proceed as follows: D*PS=0.0062. Load with thisduration equals installed capacity, K, and K =8000! ! 50,000D*PS=7691. Maximum loadshed =LS=8000! ! K ! ! 100 =209. Duration of load shedding =DLS=LS'50,000. Cost of loadshedding =DLSLSVLL'2 =$4,380.Figure 2-4.2Equilibrium ICap andload shedding inExample 3.only $1,856/h. Installing this much capacity would completely eliminate loadshedding and any need for the 100 MW of load reduction. For a cost of $1,856/h,more than $4,380/h could be saved.4 This is neither an optimal policy nor a marketequilibrium. Example 3 simply illustrates that the regulatory equilibrium inducedby setting price to the last market-clearing price before failure is far from optimal.The optimal duration of load shedding, D*LS is given by FCpeak'VLL (Result2-3.1), which in this example is $6'$10,000, or 0.06%. It corresponds to aninstalled capacity of 7870 MW. In the present example, the policy of setting priceto the last market-clearing price when the market fails to clear results in reliabilitycosts that are above optimal. They are even higher than under the naive policy ofbuilding installed capacity to the point where neither load shedding nor loadelasticity ever comes into play. In Example 3, market-based regulation is worsethan old fashioned regulation with regard to reliability policy.The Last Clearing Price Can Be Too HighWhen the last clearing price is $1,000/MWh, peakers are paid too little during timeswhen the market fails to clear and load must be shed. Consequently, load sheddingmust last longer than optimal for the price-spike revenue to equal the fixed costsof peakers.The choice of $1,000/MWh for the demand-side bid was arbitrary, and thehighest bid could easily be $100,000/MWh. If a customers computer uses 100 W,and the expected interruption would last only 0.1 hour, and the customer is willingto pay $1.00 not to be interrupted, this use of power has a value of $100,000/MWh.Entering one such bid into the market would cause the system operator to set themarket price to $100,000/MWh during all periods of load shedding. Because thisis higher than VLL, peakers would be paid too much during these times and therewould be too little load shedding. The system would be overbuilt. The same pointcan be made another way. Customers as a group should not have to pay more thanVLL, when power is only worth that much to them on average. The value of lostFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.150 PART 2 PriceSpikes, Reliability, and Investmentload, VLL, serves as an upper limit on what the system operator should pay forpower.This and the previous example make clear that the last market-clearing price,or the highest demand-side bid, is simply irrelevant to correct pricing. The correctprice to set when the market fails to clear and load is shed is the cost to consumersof shedding load, VLL. This is the best proxy for the demand curve that is missingbecause of the first demand-side flaw: the lack of metering and real-time billing(see Section 1-1.5). (While VOLL pricing is optimal under the Simple Model ofReliability it has two detrimental side effects when considered in a broader context.)

Result 2-4.5 Do Not Cap Prices at the Highest Demand BidWhen the market fails to clear and it becomes necessary for the system operatorto set the real-time market price, the last market clearing price should not be usedas it is irrelevant and can be either too high or too low. By extension, the highestdemand bid should also not be used.2-4.5 HOW REAL-TIME PRICE SETTING CAPS THE FORWARD MARKETSExample 2 demonstrates that, due to the second demand-side flaw, contemporarypower markets may fail to have a long-run equilibrium. Such markets will periodi-cally fail to clear and then will determine no market price. The system operatorwill be forced to set the real-time market price, and its price setting should havea limit no great than VLL. Whatever the limit, it will be referred to as the price cap,or Pcap, for reasons that will become apparent.A purchase-price limit on the system operator is not a price cap or price controlof the type used in other markets. It is not a restriction on private parties but issimply a rule governing the system operators actions. The system operator isinstructed to pay no more than Pcap for power and to charge no more than Pcap forpower. No unusual restrictions are imposed on private parties by this rule. Theycan offer to sell power to the system operator or to any other private party at anyprice they choose. Similarly customers can pay whatever they want for power. Inparticular, if Pcap is $10,000/MWh, any load may contract with any generator atany time to buy power for $20,000/MWh.Extraordinary rhetoric has surrounded such a price limit. These limits have beentreated as a dire threat to investment and a contradiction of free markets. In fact,this limit comes into play only when the systemoperator is forced to purchase poweron behalf of load. In this case, it is natural to limit the amount paid at least to thevalue of the power to load. Nothing is a more normal part of market operation.What is extraordinary about the system operators limit on purchase-price isthat through voluntary actions on the part of other purchasers it effectively capsthe price in all forward markets. This is not due to regulation but rather to thesecond demand-side flaw. The market would be better off without this flaw, butits existence does not suggest the need for irresponsible purchasing behavior onFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-4 Limiting thePriceSpikes 151the part of the system operator. With or without the flaw, the system operator shouldpay no more than the power is worth.The Second Demand-Side Flaw Caps the MarketBecause it is required to break even, the system operators price limit is the samefor selling as for purchasing. Thus if it pays Pcap for power it will sell it for no more.Knowing this, all power customers realize they can buy power in the real-timemarket for at most Pcap. Given this backstop price, they will pay no more for powerin advance. This simple logic caps the price in every forward market even thoughthere is no rule against customers paying more or suppliers charging more. Custom-ers know it would be a waste of money and choose not to pay more than Pcap.How does the second demand-side flaw enter this process? Consider a customerwith a high value for reliability who might be willing to pay $100,000/MWh duringa period of load shedding to be sure of obtaining the necessary power. The customerrealizes it would never need to pay more than Pcap for power but decides to signa contract for $20,000/MWh with a supplier who guarantees always to keep a spare50-MW generator as spinning reserve just for this customer. Eventually the dayof reckoning arrives and the system suffers a major outage just as load is risingtoward its afternoon peak. The alert customer phones his supplier to check on thereadiness of his private spinning reserve and is assured that all is well. The supplierthen phones the system operator to say that, if necessary, it is prepared to supplyan extra 50 MW of power in case the systemoperator has any intention of sheddingits prized customer.Unfortunately, there may not be a systemoperator anywhere that could respondeffectively to such a call. Typically the supplier would be told that the systemoperator does not control which load is shed. When the supplier calls his customerslocal utility, which is in control of load shedding, he will be told that if the customeris next to a police station he may be in luck but otherwise it is simply a matter ofchance and the die has already been cast. When load is shed, contracts betweenprivate parties are never taken into account as this is not currently possible. Whena local area is shut off, there is no way for the utility to leave one customer in themiddle of the area connected. Such a pattern of disconnection would require flippingby hand the main circuit breaker of every customer in that area except the onecustomer with the special contract.The inability of contemporary power systems to enforce bilateral contracts inreal time is the second demand-side flaw. It prevents the individual purchase ofreliable power if that power must be transmitted through the power system. Thisinability means no customer can pay more and thereby obtain more reliability thanit obtains by simply taking power from the system in real time.This does not mean all customers will wait for the real-time market to buy theirpower. They can buy it with less risk, and quite possibly a little cheaper, by purchas-ing it in a bilateral forward market. But if the price in those markets were to exceedPcap, customers would shun them and wait to buy from the system operator in realtime.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.152 PART 2 PriceSpikes, Reliability, and Investment5. Besides regulation, a number of other legal considerations set a cap on prices, with bankruptcy beingone example. Consequently, real markets may have an equilibriumthat relies on such price caps. Forexample, the equilibriummight involve periodic bankruptcies. Such equilibria are ignored here.The Price-Cap ResultThis theory of price-capping forward markets was well tested in California.The price limit in the CA ISOs real-time market varied between $250 and $750during the life of Californias day-ahead market, the Power Exchange. Becausethis mechanism was not understood, the Power Exchange had its own price capof $2,500. Although there were small discrepancies explainable by various penaltieson real-time trading, the Power Exchanges day-ahead price was always cappedquite accurately by the ISOs far lower real-time price limit.

Result 2-4.6 The Real-Time Price Limit Effectively Caps the Entire MarketThe second demand-side flaw causes the system operator's limit on the price paidfor power purchased on behalf of load to effectively cap the real-time powermarket as well as all forward markets, both public and private. The mechanismof the capping is voluntary arbitrage behavior on the part of power customers.2-4.6 TECHNICAL SUPPLEMENT: THE CONDITION FOR FAILUREExample 2 demonstrates that a contemporary market can lack a long-run equilibriumwere it not for regulatory price-setting when its supply and demand curves fail tointersect. Example 1 shows this failure is not a necessary result of the two demand-side flaws: (1) unnaturally low demand elasticity, and (2) an inability to enforcebilateral contracts in real time.This raises a question: Under what conditions will the market fail to have a long-run equilibriumwithout regulatory price intervention.5 A second question of interestis when will regulatory price intervention be beneficial in spite of the existenceof a long-run equilibrium. Both questions can be answered within the frameworkof the Simple Model of Reliability, which does not take account of the side effectsof high price spikes.Let K be installed capacity and Lg augmented load. Let Lg-max be the maximumpossible value of Lg. The dependance of Lg-max on K due to demand elasticity isexpressed by Lg-max(K). Let Rspike(K) be the price-spike revenue.

Result 2-4.7 Conditions for the Failure of a Power MarketA market without regulatory price intervention will have a long-run equilibriumif and only if there is a K such that Rspike(K) >FCpeak and Lg-max(K) <K.A market with a long-run equilibrium and without regulatory price interventionwill have a market clearing price, Pmax, at all times. If this price is lower then VLL,then the best that can be done (ignoring problems of risk and market power) is tolet supply and demand determine the price. If Pmax is higher then VLL there is noreason to instruct the system operator to pay more than power is worth, so aFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-4 Limiting thePriceSpikes 153regulatory price limit should be placed at VLL. Even with Pmax<VLL, it may bepossible to increase efficiency by improving the operation of the demand side ofthe market. Result 2-4.8 is only meant to indicate that efficiency cannot be increasedby setting a price limit because the appropriate price limit would not be binding.

Result 2-4.8 Conditions for an Efficient Power MarketIf a power market has a long-run equilibrium and no regulatory price intervention,its prices will be efficient if and only if Pmax<VLL.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. For a discussion of generation adequacy and VOLL pricing in the U.S. context, see Hirst and Hadley(1999).Fifteen years ago I used charred paper and card in theconstruction of an electric lamp on theincandescent principle. I used it too in theshapeof a horse-shoeprecisely as you say Mr. Edisonis now using it.Joseph Swanin a letter to Nature, January 1, 1880Thereyou haveit. No sooner does a fellow succeed in making a good thing than someotherfellows pop and tell you they did it years ago.Thomas Edisonin replyChapter 2-5Value-of-Lost-Load PricingSHEDDING LOAD IS AN EXPENSIVE WAY TO CURB DEMAND. It makesno distinction between those who need the power most and those who need it least.Because most customers usage is not metered in real time, and because most donot know the price, contemporary markets have little ability to ration demand withprice. Instead, when it is necessary, the system operator must ration demand byshedding load. In this case, the value of another megawatt of power equals the costimposed by involuntary load curtailment. This value is called the value of lost load,VOLL.Basic economic theory says it is efficient to pay suppliers the value of supplyinganother unit of output. Because VOLL is very high, perhaps above $10,000/MWh,this implies a very high price whenever load must be shed. Implementing this policycauses extreme price spikes, but these will be brief and lead to optimal investmentin generating capacity and optimal reliability.1 Although basic theory ignores riskand market power, it provides valuable insights and a basis for discussing moresubtle theories of setting energy prices.Chapter Summary 2-5: Because of the two demand-side market flaws, powermarkets are not yet able to use market forces to determine an appropriate reliabilitylevel. Some authority must estimate VOLL or some other determinant of optimalreliability. All such approaches are based directly or indirectly on VOLL, so theconsequences of error in the estimated value of VOLL cannot yet be avoided. Theseconsequences are not dramatic and can be reduced by overestimating VOLL. Pricerisk and market power are negative side effects of VOLL pricing.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-5 Value-of-Lost-Load Pricing 155Section 1: Valuing Lost Load. The most straightforward approach to theproblem of price caps makes the regulator act as a surrogate for load by settingprice when power is being shed. The appropriate price equals the average valuethat shed load places on power. This is termed the value of lost load, and althoughit can be well defined, it is very difficult to estimate.Section 2: VOLL Pricing Is Optimal in The Simple Model of Reliability. Under the reliability assumptions of Chapter 2-3, setting price equal to the averagevalue of lost load, VLL, will induce competitive suppliers to invest in an optimallevel of generating capacity. This does not account for the negative side effectsof VOLL pricing.Section 3: Practical Considerations. VOLL pricing is often avoided becauseof the difficulty of estimating VLL, but until the demand-side flaws of presentmarkets are sufficiently corrected, there is no way around this problem. Somereliability level must be chosen, and this is the most accurate method available.Price risk and the exacerbation of market power are both significant problems withVOLL pricing.Section 4: Technical Supplement. If VLL is estimated at $15,000/MWh butdiffers from the true value, the resulting power system will be inefficient. If thetrue value is 10 times higher, the resulting excess cost of unreliability wouldprobably be significant but less than 10% of the total cost of power.2-5.1 VALUING LOST LOADIn the most critical circumstance, when supply has reached its maximum and loadis being shed, the system operator must choose how much to offer for additionalsupply. The standard regulatory choice is to offer to pay the cost of additionalgeneration. The market approach is to offer the value that customers place on notbeing cut off. This value might be $10,000/MWh while the cost of the last unit ofpower produced might be only $500/MWh. If the market is perfectly competitive,the cheaper approach is to offer $10,000/MWh and pay this much whenever loadis actually shed. This is the price determined by the intersection of supply anddemand. Setting the price of energy in the spot market to this price whenever loadhas been shed is VOLL pricing. This result depends on competition to preventmarket power, on risks of extreme prices being costless, and on the assumptionsof the Simple Model of Reliability described in Section 2-3.3. Even with theserestrictions, the result provides a basis for a more realistic analysis and explainswhy paying more than VLL, as suggested by no-price-cap advocates, is counterpro-ductive.VOLL Pricing is Regulatory. To apply VOLL pricing, the value of lost loadmust be determined. Because most customers do not respond directly to real-timeFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.156 PART 2 PriceSpikes, Reliability, and Investment2. Australias National Electricity Code Administrator reports that Research by Monash Universityindicates that the value of lost load to end-use customers is in a very wide range of $1,000 to$90,000/MWh. (See NECA 1999b, 10.)prices, there is almost no market information on the value of lost load, and availableestimates are highly inaccurate. Consequently, VOLL pricing sets a regulated, nota market, price.The cost of load shedding is great because load is arbitrarily disconnected bythe system operator rather than demand being voluntarily reduced by customersin response to the market price. Blackouts shed high-value loads and low-valueloads in proportion, so when load needs to be shed, a load that values its powerat $100,000/MWh is just as likely to be shed as one that values it at $200/MWh.VOLL pricing, together with its inevitable blackouts, is highly inefficient relativeto a market that could rely on real demand elasticity. The claims for this policymust be judged relative to the current demand-side flawsit is optimal only aslong as they cannot be eliminated.The Problems of Estimation. The largest impediment to determining VOLLis the dramatic variation in values between customers and fromone time to another.2The effect of the duration of a disconnection on cost is also typically quite nonlin-ear. Often the first few seconds are the most costly but in other cases costs growat an increasing rate with the duration of the outage. Because most of these costsinvolve no market transactions, they are particularly difficult to evaluate.

F FF Fallacy allacy allacy allacy 2-5.1 VOLL Cannot Be Usefully DefinedBecause the value of lost load depends on the customer, the time of the loss, andthe nonlinear dependence of loss on the duration of the loss, no useful definitionof VOLL is possible.In spite of measurement problems, the concept of VOLL is well defined.Consider a given system with a given level of installed capacity and a giventransmission system. The system will be subject to random load shedding due tocontingencies, and each event will have a different average cost per MWh of lostload. Fortunately, the details of this process are irrelevant. Generating capacity isnot built to prevent any particular incident in which load is shed but to avoid thelong-run average cost of load shedding. This expected long-run average is whatis meant by the value of lost load. Conceptually, if the system could be operated for many years with its presentpattern of load and its present installed capacity, then the accumulated MWh oflost load divided by the total loss of value to consumers would equal average VOLL.But this average value is slightly different from the marginal definition of VOLLthat is needed for pricing policy. Marginal VOLL measures the decrease in lostload divided by the decrease in lost value when installed capacity is increased bya small amount.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-5 Value-of-Lost-Load Pricing 1573. To obtain this revenue fromcustomers, it would be necessary for a perfectly discriminatingmonopolist to set price at different levels for different MWh of power. This revenue is the most consumerswould pay voluntarily.

Definition Value of Lost Load (VLL)In a given system, let H be the average MWh of load that is shed and VH be theaverage net social value of producing and consuming power. Let dH be theincrease in H, and dVH the reduction in VH, caused by a small increase in installedcapacity. Then, VLL=dVH'dH. Technically, this is marginal VOLL, but it is theappropriate VOLL for present purposes and will be referred to simply as VOLL.VLL is difficult to estimate, and defining the concept carefully does not lessenthis difficulty; however, it does allow the development of a theory of price regula-tion in the face of market failure. The next section shows that VLL is the right pricefor inducing the investment needed to provide minimum-cost reliability.2-5.2 VOLL PRICING IS OPTIMAL IN THE SIMPLE MODEL OF RELIABILITYSection 2-3.3 developed the condition for optimal load shedding under the SimpleModel of Reliability, but it did not investigate the market equilibrium. This sectionshows that the equilibrium condition is the same as the optimality condition, soa competitive market will build the right amount of installed capacity. It willminimize the combined cost of energy and blackouts. Before considering the marketequilibrium, the connection between VOLL and the markets demand curve isexamined.Connecting VOLL to the Demand CurveMarkets give optimal outcomes when they are competitive and have demand curvesthat truly reflect consumer preferences. Because of the first demand-side flaw(Section 1-1.5) power-market consumers do not express their true demand and sothe system operator needs to buy power on their behalf. This precludes the optimaloutcome promised by Adam Smith and modern economics for competitive markets,but the use of VOLL pricing proves to be the best strategy given the limitationsof the markets structure. This result can be understood by investigating the relation-ship between VOLL and the true consumer demand curve.Most customers cannot respond to daily price fluctuations, so the short-rundemand curve is unobservable. If consumers were charged real-time prices andcould respond to them without transaction costs, they would use much less powerat sufficiently high prices. As a crude approximation of this unobservable demandcurve, assume that demand for power is zero at $30,000/MWh and increases linearlyto 20,000 MW at the retail price of power (see Figure 2-5.1). The area under thiscurve measures the total value of power to consumers, the consumer surplus, inthe sense that consumers would pay that value for power but no more.3 When thevariable cost of power is subtracted, the result is the total surplus of producing andFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.158 PART 2 PriceSpikes, Reliability, and Investment4. This is not a long-run calculation but represents the consumer surplus relative to a suddendisconnection.Figure 2-5.1The market demandfunction and the valueof lost load.consuming that power (see Section 1-5.2). When load is shed there is a reductionin total surplus.When load is shed, customers are disconnected without regard for the valuethey place on power. Consequently, the best assumption is that the demand curveof those remaining on the system is a scaled-back version of the complete marketdemand curve. As an example, Figure 2-5.1 shows the demand function scaled back10%. Since demand of every value is scaled back 10%, the total reduction in netsocial value is $30,000,000/h. Dividing this by the 2000 MW of load shedding givesthe (net social) value of lost load, which is $15,000/MWh4. Because consumersurplus is so much greater than the variable cost of power, and because consumersurplus is such an uncertain value, the distinction between consumer surplus andtotal surplus can be ignored.The reduction in consumer surplus caused by 1 MWh of shed load is VLL. Whenload shedding is optimal, a reduction of installed capacity would cost consumersas much in lost value as would be saved by the reduction in capacity. Accordingto Equation 1-3.2, the average cost of supplying peak energy during the period ofload shedding is ACE=FCpeak'DLS+VCpeak. Given the approximate nature of thepresent calculation and the smallness of VCpeak relative to FCpeak'DLS, the variable-cost term can be ignored. Thus, the condition for optimal load shedding isLost consumer surplus =savings from reduced capacityVLL=FCpeak'DLSSolving for DLS gives the condition for optimal load sheddingD*LS=FCpeak'VLL(2-5.1)which is exactly Result 2-3.1.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-5 Value-of-Lost-Load Pricing 159Is the Market Equilibrium Optimal?Having characterized the optimal duration of load shedding, the market equilibriumunder VOLL pricing must now be examined to see how it compares. Result 2-2.2gives the long-run equilibrium condition for investment in peakers asFCpeak=Rspike.The right side is the price spike revenue, which in this case is VLL DLS. Solvingfor the equilibrium duration of load shedding gives DeLS=FCpeak'VLL, so equilib-rium and optimal load shedding are the same.

Result 2-5.1 Within the Simple Model of Reliability, VOLL Pricing Is OptimalUnder the Simple Model of Reliability defined in Section 2-3.3, which ignoresboth risk and market power, VOLL pricing would induce optimal investment ingenerating capacity and thus optimal reliability. This assumes an optimal short-run security policy.2-5.3 PRACTICAL CONSIDERATIONSThe first concern with VOLL pricing is the difficulty of estimating VLL. Becausesuch estimates are probably accurate only to within a factor of 10, they are usuallyassumed to be useless. But the consequences of misestimation are relatively smalland currently unavoidable. If the true value of VLL is 10 times greater than theestimate used to set price, the consequent net cost of excess unreliability mightbe 10% of the wholesale cost of power (4% of retail costs). If the error were in theother direction, the cost of excess reliability would be at least three times smaller.These values are based on a conservative estimate for the PJ M market and anestimated VLL of $15,000. Details are given in Section 2-5.4, the Technical Supple-ment. A more precise estimate might well indicate that the costs were considerablysmaller.

Result 2-5.2 Inaccuracy of Estimation Does Not Rule Out the Use of VOLLSome reliability level must be chosen, and as a flawed demand-side prevents themarket from determining reliability, no more accurate method of selecting a levelis available.Although misestimation of VLL may waste as much as a few percent of totalpower costs, the use of VLL should not be rejected until a better alternative isavailable. Instead of estimating VLL, D*LS might be estimated directly and this couldbe used to determine reliability policy. But D*LS cannot be estimated without usingVLL, so nothing is gained. Similarly the optimal value of installed capacity may beestimated. But what makes such a value optimal? Only the fact that it minimizessystem costs plus the cost of lost load, so again, no estimate of K* is possiblewithout an estimate of VLL. The only way out of this dilemma is to fix the demandFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.160 PART 2 PriceSpikes, Reliability, and Investment5. This approach to calculating VOLL is suggested in NECA (1999a).6. If VOLL changed due to a change in customer technology, e.g., battery backups for all computers, thiswould not affect the trade-off between voluntary clearing and price risk. This trade-off is simplyunrelated to VOLL and to any meaningful economics.side of the market and let the market determine optimal reliability. Until then, afew percent of inefficiency must be accepted.Those concerned about the poor quality of the estimate of VLL have sought otherrationales and other ways of setting the value of the price cap. The two most popularconsiderations are supply-side costs and risk.Supply-Side Calculations. Engineers have reliability standards which are notderived from explicit calculations of consumer surplus and so they have no basisin economic theory. Nonetheless, they are derived from common sense and yearsof experience and should not be discarded until a better approach is available.Engineers have found it costs very little to reduce the duration of shed load to aboutthree to five hours per year and, at such a level, customers do not complain much.The fixed cost of a peaker, which is roughly $50,000/year, when divided by fivehours per year, gives a price of $10,000/MWh. This is the so-called VOLL priceneeded to induce investment up to the point where load shedding is reduced to fivehours per year.5

Of course, this is not an estimate of the value of power to consumers; it is anestimate of what price is required to reduce load shedding to five hours per year.If this is a desirable level of reliability, it is because actual VLL is near$10,000/MWh. The calculation of VOLL from a choice of load-shedding durationand the price of peaker technology is only reasonable if a lack of customer com-plaints is a reasonable indicator of optimal load shedding. In other words, thenormal engineering procedure that starts with some arbitrary acceptable durationof load shedding, say one day in ten years, is simply a crude estimate of the VOLLtrade-off.Risk. Risk is another matter. It provides no means of computing an appropriatelevel for VOLL and no information about reliability. It is, however, an importantconcern. This is recognized explicitly in the Final Report of Australias ReliabilityPanel (NECA, 1999b, 6).The core principle that must be met in establishing the level ofVOLL has been identified as balancing the ability of the marketto clear voluntarily, i.e. for supply to match demand, under allbut the most extreme conditions, against risk.This core principle has nothing to do with establishing the level of VOLL, butrisk is correctly seen as an important problem.6 For this reason, the Reliability Panelproposed that if revenues from VOLL pricing exceed $300,000/MW in a 7-dayperiod, the price cap should be temporarily dropped from $20,000 to $300/MWhon peak and to $50/MWh off peak (NECA 1999c). In this view, risk is a necessaryevil, and it must be limited.Unfortunately the section of the Final Report that is devoted to risk begins byexpressing the opposite view (p. 12).February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-5 Value-of-Lost-Load Pricing 1617. There is one indirect way in which risk may be socially useful. Risk will induce the signing of morelong-termcontracts, and long-termcontracts reduce market power in the spot market. This conclusionignores any impact on long-run market power, so further study is needed.The NECA capacity mechanism report discussed the essentialrole risk and efficient risk management play in an energy onlymarket, in particular as a driver for reliability. The reliance oncommercial price signals to provide incentives to participantsto influence market behavior centres on risk.Although there is no necessary contradiction between these two views (risk couldbe good for one reason and bad for another), the latter view is incorrect. Risk togenerators makes investing more expensive, and risk to customers has similar costs.Also, the inevitable demand-side risk-management contracts mute the accurateincentives of the extreme VOLL prices. This is not to say that customers are wrongto avoid risk; they are not. Risk is a cost, not a benefit. The many contractualresponses to the risks of VOLL pricing indicate that market participants go to agreat deal of trouble to avoid the risks it imposes because risk is costly.

F FF Fallacy allacy allacy allacy 2-5.2 Risk from VOLL Pricing is BeneficialBecause the risk of extreme price swings gives the market an opportunity to sellnew products to ensure customers against the imposed risk, imposing these riskson the market is socially beneficial.The concept of risk is frequently misunderstood, but there is a simple test forwhat is caused by risk and what is not. Market participants can be of two types:risk averse and risk neutral. A participant who is risk neutral does not respond torisk (the standard deviation of price) but instead responds only to average prices.No behavior exhibited by a risk-neutral party can be a response to risk.The beneficial incentive properties of VOLL pricing are not due to risk butsimply to the costs it imposes and the profit it delivers when price is high. A risk-neutral consumer will cut consumption when the price is high, and a risk-neutralinvestor will build peakers and keep them ready at a moments notice to captureVOLL prices. This proves that these beneficial responses are in no way due to risk.The model in the previous section assumed risk-neutral suppliers and consumers,and the result was optimal. Had risk aversion been included, the result would havebeen suboptimal, due to the costs of risk.7Market Clearing. The various NECA reliability reports frequently refer to theability of the market to clear voluntarily and, as quoted previously, elevate thisto the core principle of VOLL pricing. Market clearing is a key economic princi-ple, but it is not an end in itself. In this case the approach to market clearing canbe carried too far. Because demand cannot yet respond effectively to real-timeprices, it makes sense to have the system operator bid some average value on theirbehalf. By bidding $1,000,000/MWh, the operator could ensure that the marketcleared for all but five minutes per year (as an average over many years). This wouldnot be an improvement. Ideally, there should be some load shedding because itis cheaper than buying reserve generation. When load is shed, the market has notFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.162 PART 2 PriceSpikes, Reliability, and Investment8. J oskow (2001a) makes a similar suggestion. . . . the combination of relatively tight supplies andextremely inelastic demand means that prices can rise to extraordinary levels and are much moresusceptible to market power problems than when supplies are abundant.cleared. Until the market flaws described in Section 2-3.1 are removed, the goalis to have the optimal, not the minimal, number of nonclearing hours.Long-Run Incentives. Adequate investment in generating capacity is the centralgoal of VOLL pricing. It is a long-term process that has no need for incentives thatchange drastically from minute to minute or even from month to month. VOLLprice spikes are not needed to encourage adequate generation investment. In fact,VOLL payments are extremely risky and this makes investing more expensive. Theriskiness is not due to the hourly price fluctuations but rather to the annual fluctua-tions in price-spike revenue. If the five hours of price-spikes were made up of 50independent 6-minute events, revenues would be quite dependable. But they aremade up of very few events. Consequently, VOLL price-spike revenue fluctuatesdramatically from year to year and is difficult to estimate.Short-Run Incentives. VOLL pricing is not needed to induce generators toprovide spinning reserves. Spin must be provided in advance of a contingency andso before the price increases. When price does jump to VLL, generators provideenergy, not spin. In other words the possibility of P =VLL raises the expectedprofitability of providing spin. Of course the same effect can be achieved by payingthem this expected value with certainty instead of on average. Once generators arespinning, a price of $15,000/MWh will certainly induce them to provide energybut so will a somewhat lower priceprobably $300/MWh would work just as well.VOLL pricing is most advantageous as a short-term incentive for demandreduction, which can require a genuinely high price. Unfortunately, many risk-management schemes will severely curtail this incentive. Many customers will optnot to see the real-time price, and for now most cannot see it. In these cases VLLis useless as a short-run incentive. But well-designed contracts can reduce customerrisk dramatically while leaving the VOLL incentive in place, and eventually muchmore load will be metered. Load may become quite price-elastic, and most of thebeneficial reduction in required generating capacity may come fromloads responseto prices 20 times lower than VLL. Still, when load has to be shed, VOLL providesthe correct incentive for customers to reduce demand.Market Power. Perhaps the greatest drawback to VOLL pricing is not risk butmarket power.8 Consider 2 possible price caps, 1 at $500 and 1 at $20,000. Considera supplier with all of its 2000 MW of generation dispatched and an average variablecost of $50/MWh. Assume that the market price is $100, which is the marginalcost of the marginal plant. The supplier in question is earning a short-run profitof $50/MWh on its 2000 MW for a total of $100,000/h.Suppose load is 18,200 MW and available supply is 20,000 MW. If the supplierwithholds 1900 MW it can push the price to either $500 or $20,000, dependingon the cap. At $500 it would earn $450/MWh on the 100 MW it still has in produc-tion, which comes to $45,000/honly half of what it earns at full output. At$20,000 it would earn $19,950 on 100 MW, or $1,995,000/h, which is almost 20times more than it earns at full output. With a $500 price cap it loses profit byFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-5 Value-of-Lost-Load Pricing 163Figure 2-5.2An unusually steep load-duration curve.attempting to exercise market power. With a $20,000 price cap it makes enormousprofits by exercising market power. VOLL pricing provides strong incentives forthe exercise of market power.2-5.4 TECHNICAL SUPPLEMENTMisestimating VLL may cause a relatively small decrease in the overall efficiencyof the power market. To demonstrate this, assume that VLL has been estimated tobe $15,000/MWh and consider two possibilities: (1) actual VLL could be$1,500/MWh, or (2) it could be $150,000/MWh. How much inefficiency is associ-ated with each possibility?Using $6/MWh for the fixed cost of a peaker as in previous examples and thethree values of VLL, three optimal load-shedding durations may be calculated usingEquation 2-5.1.Table 2-5.1 Results of Errors in Estimation of VOLLVOLL Duration, D*LSK in MW Comment$150,000/MWh D*LS= 0.35h/year 55,000 Possible optimal value$15,000/MWh DeLS= 3.50h/year 50,000 Assumed value$1,500/MWh D*LS= 35.04h/year 45,000 Possible optimal valueThese optimal durations must be translated into installed capacities using a load-duration curve. The steeper that curve, the greater the error in the installed capacitylevel and thus the greater the resulting inefficiency. PJMs load-duration curve willbe used for this example after exaggerating its steepness enough to prevent anychance of underestimation. The installed capacity levels corresponding to thecalculated durations are shown in Table 2-5.1.If the true value of VLL is $150,000, then 5000 MW too little capacity wouldbe installed with the result that too much load would be shed. From Figure 2-5.2it can be seen that excess load shedding would be less than one third of 3.5 h5000MW, or about 7000 MWh. Using the true VLL of $150,000 and dividing by 8760h/year gives a reliability cost of $120,000/h. If the true value of VLL is $1,500, thenFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.164 PART 2 PriceSpikes, Reliability, and Investment5000 MW too much capacity would be installed with an excess fixed cost of$6/MWh5000 MW which equals $30,000/h.Returning to the first possibility, the cost of the extra lost load is partiallycompensated for by the reduced cost of installed capacity, again $30,000/h. So thenet excess reliability cost in this case is $90,000/h. The total cost of serving loadin PJ M is about $30/MWh30,000 MW, or $900,000/h. If VLL was actually$150,000, while VOLL pricing was based on an estimated VLL of $15,000, theresulting excess reliability cost would be 10% of the total cost of power. Becausethe steepness of this load-duration curve has been exaggerated, the actual cost ofsuch a mistake in PJ M might be considerably less.In conclusion, it would appear to be safer to over-build than to under-buildrelative to an estimated level of VLL. Either a dramatic underestimation of VLL ora dramatic overestimation of the optimal duration of load shedding (3.5 h/year when0.35 h/year is the correct value) would result in a significant, though not dramatic,cost of unreliability.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. This plant preceded Edisons invention of the electric light and opened three years before EdisonsPearl Street power stationthe first central station. Charles Brush lit Broadway, New York fromacentral station in 1880. (See http://www.pge.com/009_about/past/&e=921.)By September [1879] a littlebuilding at Fourth and Market was completed and two tiny Brusharc-light dynamos wereinstalled. Together they could supply 21 lights. Customers wereluredby theunabashed offer of servicefrom sundown to midnight (Sundays and holidays excluded)for $10 per lamp per week. Yet in light-hungry San Francisco, customers cameclamoring. Bythefirst of thenext year, four moregenerators with capacity of morethan 100 lights had beenadded. Electricity had cometo theWest.1Pacific Gas and ElectricOur HistoryChapter 2-6Operating-Reserve PricingOPERATING RESERVES ARE NEEDED TO SOLVE VERY SHORT-RUNRELIABILITY PROBLEMS, BUT THEIR PRICING CONTROLS THE LONGRUN AS WELL. Engineering suggests appropriate levels for operating reserves,but it cannot, on its own, determine what price to pay for them. Surprisingly, theirprice should depend on the value of lost load (VOLL) and on long-run, more thanshort-run, reliability considerations. By setting prices to a relatively modest levelwhen the system is short of operating reserves, rather than to the extremely highvalue of VOLL when the system is short of capacity, operating-reserve (OpRes)pricing can substitute for VOLL pricing. This opens up a wide range of policyoptions which can be used to solve some of the most pressing problems of todayspower markets.1Chapter Summary 2-6: A market with randomshifts in the annual load-durationcurve is examined to compare the side effects of high and low price spikes. Highprice spikes are found to cause investment risk and to encourage the exercise ofmarket power. Low spikes are just as effective as VOLL pricing at encouragingoptimal investment in generation capacity. High price spikes are more useful onthe demand side than on the supply side, so different price limits should be usedfor the two sides of the market.Section 1: Less Risk, Less Market Power. In a market with two load-durationcurves, one for hot years and one for normal years, short-run profits are foundto fluctuate between zero and 400% of normal under VOLL pricing but onlyFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.166 PART 2 PriceSpikes, Reliability, and Investment2. This statement considers PJ M as an isolated system, which it is not, and so ignores the opportunity costof not selling power out of PJ M. Competition between systems is analyzed in Chapter 2-9.between 80% and 160% of normal under OpRes pricing. One supplier selling 5%of total ICap into the spot market would exercise enough market power under VOLLpricing to raise the average price of power by more then $50/MWh but could raiseit only by $5/MWh under OpRes pricing.Section 2: How Can OpRes Pricing Be Better than Optimal? VOLL pricingis optimal according to simple economic theory because it offers to pay what poweris worth. This is an advantage of VOLL pricing if there are sources of supply ordemand that would respond to the $15,000 VOLL price but not to a $500 OpResprice. This advantage must be traded off against the negative side effects of highprice spikes. The best solution would be to allow high demand-side prices whilekeeping supply-side prices relatively low.2-6.1 LESS RISK, LESS MARKET POWERMarkets that do not use VOLL pricing usually have an operating reserve (OpRes)requirement backed by high prices; this will be called OpRes pricing. These pricesare often higher than needed to attract operating reserves from the local market,but they serve to compete with other control areas for reserves and to induceinvestment in generating capacity. PJ M has never had a generator in its market thatwould not provide operating reserves for a price of $200/MWh. Yet if PJ M runsshort of reserves, it offers to pay up to $1,000/MWh to any generator that has bidthat high.2This section compares VOLL pricing with OpRes pricing in three dimensions:(1) equilibrium installed capacity, (2) risk, and (3) market power. To model risk,randomness is introduced into the load-duration curve. Two such curves arespecified, one for hot years and one for normal years. Hot years could be yearsthat are literally hot or that have unusually high load or generator outages for otherreasons. Market power is modeled by assuming that one generator sells an amountof energy equal to 5% of the markets total capacity into the spot market.A Model with Risk and Market PowerThe present example is designed to have an optimal installed capacity level ofK =50,000 MW and is assumed to have a true value of lost load known to beVLL=$15,000/MWh. The fixed cost of peakers is again assumed to beFCpeak=$6/MWh. According to Result 2-3.2, the optimal duration for load sheddingis D*LS=3.5h/year. A pair of load-duration curves, one for hot and one for normalyears, are designed to give this duration for the optimal capacity level. Near peakFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-6 Operating-Reserves Pricing 1673. Duration measured in h/year is dimensionless (time'time gives a pure number) as required but mustbe divided by 8760 to produce the numeric value required in formulas using duration. (For example,1h/year =1h'8760h =0.000114.) See Chapter 1-3 for a more complete explanation.4. Pcap will often be referred to as a price cap, and although it functions as one, it is not a cap in thetraditional sense of a legal restriction on the actions of private parties. It is instead a purchase price limiton the systemoperator. See Chapter 2-4.load, these two load-duration curves (with duration measured in h/year) are givenby the following equations:3In hot years (25%): D =3.5(52!! Lg'1000)2, for Lg<52.In normal years (75%): D =3.5(50!! Lg'1000)2, for Lg<50.Values of Lg not covered by these equations have a duration of zero.Note that augmented load, Lg, which includes generation outages, hasbeen used to determine duration, so these are actually augmented-loadduration curves (see Section 2-3.3). In hot years, the peak (augmented)load is 52,000 MW, so the duration of Lg at this load level is zero, butthe duration at a load of 50,000 MW is 3.522, or 14 h/year. Becauseonly 25% of the years are hot, and because normal years have zeroduration at a load of 50,000 MW, the average duration at that load is25% of 14, or 3.5 h/year. This is the optimal duration for load shedding,which confirms the fact that K =50,000 MW is the optimal level ofinstalled capacity.One supplier in the market is assumed to have 2500 MW of capacityto sell into the real-time market. With this capacity it could earn the highspot prices generated by VOLL or OpRes pricing, or it could exercise market powerin the spot market. It could withhold, for example, 2400 MW in order to cause Lgto exceed 50,000 MW, cause load to be shed, and cause the market price to be setat $15,000/MWh thereby profitably earning $1,500,000/h on its remaining 100MW of operating generation.Equilibrium Installed CapacityAs demonstrated in Chapter 2-4, VOLL pricing induces the optimal level of installedcapacity, so comparing the two approaches requires only an evaluation of theinstalled capacity induced by OpRes pricing. This will of course depend on boththe required level of operating reserves, ORR, and on the price paid when the systemis short of operating reserves, Pcap.4Contrary to many predictions that a low price cap would prevent adequateinvestment, the two policy variables provide more than enough control to induceoptimal investment or more. For this example, ORR will be arbitrarily set to5000MW and only Pcap will be used to design an optimal pricing policy. FromResult 2-2.2, the long-run equilibrium condition for installed capacity is. Price-spike revenue equals Pcap times the duration at which price FCpeak=Rspikeis at this level. Price is at the cap whenever , i.e., when Lg>K !! ORRLg>45,000 MW. The following table presents durations for various useful loadlevels.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.168 PART 2 PriceSpikes, Reliability, and InvestmentTable 2-6.1 Durations of Load SheddingAugmented LoadDurationIn h/year In %50,000 MW 3.5 0.04%47,520 MW 33.7 0.38%45,000 MW 108.5 1.24% *43,050 MW 196.9 2.25%Table 2-6.1 shows that with ORR=5000 MW and K optimal, price will be set toPcap for 108.5 h/year, so the price spike revenue will be Rspike=0.0124 Pcap.To obtain the required price-spike revenue for a long-run equilibrium, $6/MWh,the price cap must be set toPcap=(equilibrium Rspike)'(optimal D at Pcap) =($6/MWh)'0.0124 =$484/MWh.more than 30 times less than VLL. With this price cap, and an OpRes requirementof 5000 MW, the markets long-run equilibrium level of installed capacity will beoptimal. With any higher level of Pcap, too much generation will be built, more thanwould be built with a price cap of $15,000/MWh under VOLL pricing.

Result 2-6.1 Many Different Price Limits Can Induce Optimal InvestmentIf the system operator pays only up to Pcap but no more any time operatingreserves are below the required level, a low value of Pcap will suffice to inducethe optimal level of installed capacity. The higher the reserve requirement, thelower the optimal price limit will be. Capacity requirements can further reducethe optimal level of Pcap.RiskUnder both pricing systems, price-spike revenues are high in hot years and lowin normal yearsunder VOLL pricing these fluctuations are dramatic. In hot yearsthe market price is set to VLL for 14 hours, which produces an average annual price-spike revenue of $24/MWh, four times the amount needed to cover the fixed costsof peakers. In normal years, augmented load never exceeds capacity and there areno price spikes. Peakers recover none of their fixed costs, and baseload plantsrecover only a fraction of theirs.Under OpRes pricing, the duration of high prices is 3.5 (52!! 45)2 in hot yearsand 3.5 (50!! 45)2, which is 172 and 88 hours per year, respectively. Thesedurations produce price-spike revenues of $9.48/MWh in hot years and $4.84/MWhin normal years, much less variation than occurs under VOLL pricing. While thestandard deviation of price-spike revenues is about five times greater than underOpRes pricing, a better appreciation of the difference in profit dynamics can begained by examining a sequence of years. To this end, Figure 2-6.1 displays a 40-year sequence of price-spike revenues generated by a Monte-Carlo simulation. ToFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-6 Operating-Reserves Pricing 1695. The initial string of normal years is not an artifact of this being the first draw, as Excels randomnumber generator was used extensively before this sample was drawn.Figure 2-6.1One realization of aMonte Carlo simulationof profits under VOLLand OpRes pricing.avoid selection bias, the first draw from the simulation has been presented.5 Noticethat the sequence begins with 12 years in which peakers cover none of their fixedcosts under VOLL pricing. This is rather unlucky. If the market had opened insteadin year 22, generators would have recovered four times their annual fixed costsin five of the first seven yearsa bonanza.Although the market generating these profits is in perfect long-run equilibriumevery year, investors would surely begin to doubt this after losing all of their fixedcosts twelve years running. Economics may suggest that investors are rational andwill realize this is just a string of bad luck, but the suggestion only makes senseif they have experienced this sort of phenomenon enough times to learn fromexperiencethat might take a few hundred years.Even under OpRes pricing, investors will be discouraged, but the reaction shouldset in less quickly as they will recover 80% of their fixed costs in normal years.Such a market might still require a significant risk premium, and it is worthwhileto look for a less risky design. Another factor, long-term contract cover, shouldbe considered, as it mitigates risk under both pricing schemes.

Result 2-6.2 A Lower, Longer-Duration Aggregate Price Spike Is Less RiskyA short-duration aggregate price spikes causes much more year-to-year variancein short-run profits than does long-duration aggregate price spikes.Long-Term Contracts. Generators typically sell part of their power in long-termcontracts that last anywhere from one to twenty years. If all power were sold undersuch contracts and they were rationally and accurately priced, generators wouldbe fully hedged against the vicissitudes of the spot market. Understanding this pointrequires some background in the role and operation of long-term markets.Both suppliers and consumers have a choice between buying in the long-termforward markets or buying in the spot market, and both have a preference for buyingin the forward markets so they can lock in a price and avoid the volatility of thespot market. They may also see some advantages to the spot market, such asFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.170 PART 2 PriceSpikes, Reliability, and Investmentflexibility in trading, but the behavior of power markets indicates the motive tohedge is stronger and most power will be sold under at least moderately-long-termagreements. Because both parties can choose the spot market, the long-term pricemust be quite close to the spot price. Otherwise one party will find its preferencefor certainty overcome by its preference for a favorable price and will move itstrade to the spot market.Because of this arbitrage condition, long-term contracts will reflect averagespot market prices. This is how VOLL and OpRes pricing, which apply only tothe spot market, can act with full force on the investment decisions of generators.If the spot price is high, then even though an investor plans to sell no power in thespot market, it knows this high price will be reflected fully in the long-term marketin which it plans to sell its power. Of course one years spot prices do not determinethe price of long-term contracts sold at the end of that year. Such contracts arepriced according to the expected long-run average of future spot prices. Nonetheless,if VOLL prices are expected to be high on average, long-term contract prices willbe equally high.Because long-term contracts are based on expected long-run averages, theysmooth out the year-to-year volatility of the spot market. But if spot prices areextremely low for four years at a time, which would be a common occurrence inthe present model, this will inevitably have a significant impact on long-termexpectations and prices. Thus, even if the market is in perfect long-run equilibrium(optimal installed capacity) every year, as in the present Monte Carlo simulation,fluctuations in long-run prices must be expected, and they will be more extremeunder VOLL pricing than under OpRes pricing. Because of this and the fact thatmany generators may sell significant amounts of power in the spot market or short-term markets, VOLL pricing will impose more risk on the market than OpRespricing. The random fluctuations in long-term prices, caused by runs of good and badluck in the spot market, will be reflected in long-run fluctuations in investment andin installed capacity. Consequently the market will not always be in long-runequilibrium, and this will cause even greater fluctuations in scarcity rents collectedfrom the spot markets.Market PowerIn this example, the supplier with market power is assumed to be selling powerfrom 2500 MW of capacity into the spot market. Thus, under VOLL pricing, if loadis 47,501 MW, the supplier can withdraw its capacity and force load shedding, thussending the price to $15,000/MWh. Unfortunately, this leaves no output on whichit can earn a profit.With a price increase of this magnitude, it would need only a little output tobreak even. Say its variable cost is $30/MWh and the market price is $130/MWhbefore its exercise of market power. Raising the price to VLL increases its profitper MW sold by about 150 times [(15,000!! 30)'100]. Thus it will increase itsprofits if it can raise price to VLL and retain only 20 MW of output. When load isgreater than 47,520 MW, this supplier will exercise market power and raise theFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-6 Operating-Reserves Pricing 171price to VLL. This load level will occur for 33.7 h/year in normal years which isalmost 10 times the optimal duration. Thus under VOLL pricing, the exercise ofmarket power by this supplier will raise the price-spike revenue by almost a factorof 10. The result will be a $52/MWh increase in the average cost of all power soldin this market.Under OpRes pricing, the same supplier would have more difficulty exercisingmarket power because it could increase profits by only a factor of (Pcap!! VC)'(P !! VC), which comes to 3.54, much less than the 150 times increase for VOLLpricing. Still, the supplier could withhold 77% (1950 MW) of its capacity and profitfrom the resulting price increase. Thus, whenever load increases above 45,000!!1950 MW, or 43,050 MW, which occurs for 197 h/year, the price will be set toPcap. Since under OpRes pricing, the competitive duration of the price spike is 108h/year, the increase in price-spike revenue is less than a factor of twoa little lessthan $5/MWh.

Result 2-6.3 High Price Caps Invite the Exercise of Market PowerHigh price caps allow a supplier to withhold a greater percentage of its capacityand still profit from the resulting increase in market price. Additionally, the ratioof the duration of maximum prices with and without the exercise of market poweris greater for low-duration price spikes. Because high price caps must be designedto produce low-duration price spikes, high price spikes exhibit a greater percent-age increase in duration as a result of an equal level of withholding.There are two distinct mechanisms that work together to produce increasedwithholding of capacity under high price caps. First, a high cap allows a muchgreater increase in profit fromthe exercise of market power. This allows the supplierto withhold a greater percentage of its capacity (99.3% vs. 77%) while still experi-encing a net increase in profit.Second, high price caps are necessarily associated with short-duration pricespikes; otherwise they would produce enormous excess profits. The percentageincrease in price-spike duration is greater when applying a fixed amount of capacitywithholding to a short-duration spike than to a long-duration spike. This is a generalproperty of load duration curves. For every additional fixed MW decrease incapacity, the load duration increases by a smaller percentage than for the previousdecrease. Thus, high, short-duration price spikes exhibit a greater percentageincrease in duration (10 times vs. twice) for a given amount of withholding thando lower, longer-duration price spikes.This demonstrates what appears to be a general tendency for lower but longer-duration price spikes to be less conducive to the exercise of market power. In theshort run, excess market power could result in significant transfers of wealth, butin the long run it, will simply attract new investment and increase the level ofinstalled capacity. The resulting reliability level will be difficult to predict becausethe extent of market power and the effect of withholding are difficult to predict.This phenomenon is considerably more complex than the reduction of risk underOpRes pricing and deserves further investigation.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.172 PART 2 PriceSpikes, Reliability, and Investment2-6.2 HOW CAN OPRES PRICING BE BETTER THAN OPTIMAL?Chapters 2-3 through 2-5 argued that VOLL pricing was the economically sensibleapproach. It sets the market price to the value that demand would collectively placeon power were it able to express its collective (average) valuation. The precedingexample suggests that the market price could be set 30 times lower with no illeffects. What desirable property of high, value-based prices has been overlookedin the current analysis?Economics suggests the use of VOLL pricing because it will send the rightsignals to all possible suppliers and loads. If VLL is actually $15,000/MWh and somegenerator has a variable cost of $14,000/MWh, offering to pay $15,000/MWh willprovide a net social benefit of $1,000/MWh for every MWh purchased if it is usedto reduce load shedding. With Pcap set to $500, this opportunity would be missed.The importance of such missed opportunities depends on how much generationhas a marginal cost greater than Pcap.From the perspective of taking advantage of all possible trading opportunities,VOLL pricing is optimal and OpRes pricing is suboptimal. But if the tradingopportunities missed by OpRes pricing are few and if the negative side effects ofVOLL pricing are great, OpRes pricing will be superior in the real world eventhough it is suboptimal in the simplest of economic models.The demand side of the market may contain more important missed opportunitiesthan the supply side. While generation technology is fairly uniform and known tobe capable of producing very little output at marginal costs above $500/MWh (withnormal fuel costs), the demand side is far more complex. The very definition ofVOLL, as average value, indicates there are many uses of power with higher value.So the spectrum of demand-side values can neither be limited to the low levelsassociated with the marginal costs of production nor predominately higher thanVOLL. Almost by definition, there must be a great amount of demand with valuesbetween the low levels of OpRes prices and the high levels of VOLL prices, andall of these are opportunities potentially missed by a low price cap. But the qualifi-cation, potentially, is crucial. If these opportunities were all real, the market wouldbe functioning properly and would not need a price limit. In fact, it would alwaysclear at a price far below VOLL.VOLL pricing will have a significant advantage on the demand side only ifdemand is so unresponsive to price that VOLL pricing is needed but responsiveenough that a price of $15,000 will illicit significantly more demand reduction thana price of $500/MWh. This is a possibility, and the opportunities on the demandside should not be missed if they can be captured without even more damagingside effects.Side Effects. The side effects of risk and market power are potentially serious,so the trade-off between these and the advantage of stimulating more demandresponse should probably favor low price spikes, especially until a new powermarket has clearly stabilized. Although the California market suffered fromnumer-ous flaws unrelated to its core structure, it seems quite likely that the type of profitFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-6 Operating-Reserves Pricing 173instability associated with high price spikes played an important role. During itsfirst two years of operation, profits were low and investment was discouraged. Inthe third year, augmented load in the Western region was high, both because ofrapid growth in real demand and a reduction in available hydroelectric output Theresult was very tight conditions in the California market, mostly because importsdropped by close to 4000 MW. This caused price spikes and these encouraged theexercise of market power which exacerbated both the high prices and the shortages.

Result 2-6.4 Reliability Policy Should Consider Risk and Market PowerThe right average installed capacity will provide adequate reliability, but two sideeffects of reliability policy should also be considered. Infrequent high price spikesincrease uncertainty and risk for investors which raises the cost of capital, and inextreme cases, causes political repercussions. The possibility of extremely highprices also facilitates the exercise of market power.A Separate Demand-Side CapThe obvious solution to the dilemma of needing high price spikes on the demandside and low price spikes on the supply side is to have separate caps for the twosides of the market. At most times, the market would clear and the two prices wouldbe equal. During a shortage, however, load could be charged more than generationis paid. This would result in a profit for the system operator, which would be savedin a balancing account and returned to load as a rebate spread over as many hoursas possible. In effect it would probably just reduce other distorting charges placedon load for such purposes as paying for the fixed costs of transmission and theservices of the system operator.Even though demand-side prices should be higher than supply-side prices, theyshould still be capped at VOLL or less. High prices on the demand side wouldencourage load-serving entities to develop real-time rates in order to reduce theircosts. Once such rates are in place, high prices on the demand side will serve toencourage the rapid development of price responsiveness, which will eventuallymake the demand-side cap irrelevant.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.An electrick body can by friction emit an exhalation so subtile, and yet so potent, as by its emissionto causeno sensiblediminution of theweight of theelectrick body, and to beexpanded through asphere, whosediameter is abovetwo feet, and yet to beableto carry up lead, copper, or leaf-gold, atthedistanceof about a foot from theelectrick body.Sir Isaac NewtonSamuel Johnsons Dictionary of the English Language, 1755Chapter 2-7Market Dynamics and the Profit FunctionECONOMICS FOCUSES ON EQUILIBRIA BUT HAS LITTLE TO SAY ABOUTTHE DYNAMICS OF A MARKET. Once economics shows that a system has anegative feedback loop so that there is a point of balance, it considers its job done.Engineers move beyond this stage of analysis to consider whether a system willsustain oscillations and, if not, whether it is over- or under-damped. Economicsunderstands that investment dynamics can produce cycles but has faith thatrationality will generally prevent this. It also ignores the noise sources (randomlyfluctuating inputs) that keep economic systems excited.Usually these oversights do not offer much cause for concern. In power markets,however, a 4 or 5% fluctuation in either load or capacity, coupled with the wrongpricing policy, can cause the average annual spot price to triple. Such dynamicscannot be ignored. If they are not corrected at the time of market design, they willbe reported later by the press.Many profit functions determine the same optimal equilibrium value of installedcapacity, but this means only that they agree at one point. At other points, they maydiffer dramatically, and these differences imply different market dynamics. Al-though the profit function falls far short of providing a theory of those dynamics,it does provide some basic insights which make possible a discussion of the topic.Chapter Summary 2-7: Profit functions can be calculated fromthe load durationcurve and two policy variables: the price cap and the required level of operatingreserves. Once calculated they reveal the equilibrium level of installed capacityand give some indication of the markets riskiness and conduciveness to the exerciseof market power. Thus the first step in assessing a pricing policy should be thecalculation of the associated profit function.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-7 Market Dynamics and theProfit Function 1751. The profit function gives short-run (business) profits, not long-run (economic) profits.Section 1: Calculating Profit Functions. The profit functions give expectedshort-run profits as a function of installed capacity, K. It is most convenient tocalculate them for the peaker technology, in which case short-run profit is the sameas price-spike revenue. This is determined by the price-cap level and the durationof the price spike. This duration is determined from the load-duration curve andthe required level of operating reserves, which triggers the price cap. The profitfunction is found to be much steeper under VOLL pricing than under OpRes pricing.Section 2: Interpreting the Profit Function. The profit function decreasesas K increases, eventually crossing the level of peaker fixed costs. To the left,because short-run profits exceed fixed costs, economic profits are positive and thereis an incentive to invest. To the right, profits fail to cover fixed costs, so investmentstops, while load growth continues. As a result, long-run equilibrium installedcapacity is determined by the intersection of the profit function and the level offixed costs.If the function is steep, then an increase in load, or withholding of capacity,both of which mimic a decline in K, will cause a large increase in profit. The firstimplies that steep profit functions are risky, and the second implies that theyincrease market power.2-7.1 CALCULATING PROFIT FUNCTIONSChapter 2-6 modeled a power market and two pricing limits for the systemoperator:(1) the VOLL pricing limit, and (2) the OpRes pricing limit. Under VOLL pricingthe systemoperator sets the spot-market price to VLL ($15,000/MWh in this example)whenever augmented load, Lg, exceeds installed capacity, K. Under OpRes pricing,the price is set to $484/MWh (in this example) whenever operating reserves, OR,fall below the operating reserve requirement, ORR, of 5000 MW.The market is characterized by two load-duration curves, one for hot yearsand the other for normal years, with the hot ones occurring 25% of the time andthe normal ones 75%. Together these produce a single long-run average loadduration curve which will be sufficient for the calculation of the profit functionbecause this function suppresses the year-to-year randomness examined in theprevious chapter.A profit function plots long-run average profits for a particular type of genera-tion technology, usually for the peaker technology.1 In this case, short-run profitsare equal to the price-spike revenue. As explained in Chapter 2-6, these fluctuatefrom year to year due to fluctuations in the augmented-load duration curve. Overthe long run, price-spike revenues average out, and that average exactly equals theprice-spike revenues that would result from the long-run average load-durationcurve. So, although the average load-duration curve is not correct for any particularFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.176 PART 2 PriceSpikes, Reliability, and Investment2. Each type of installed capacity has its own equilibrium condition, and it is possible to need morebaseload but less peaker capacity. Focusing on peaker investment is a simplification, but the marketprovides correct signals for the relative investment in off-peak technologies. Thus, if reliability policyinduces the right level of investment in peakers, the market will take care of other types of investment.year, it is exactly what is needed for computing long-run average price-spikerevenue, Rnspike.The purpose of constructing the profit function is to understand thefeedback loop discussed in Chapter 2-1 which controls investment andinstalled capacity. The price-spike revenue is the appropriate summarystatistic for market prices because it connects prices to investment bya very simple rule. Rnspike encourages investment when and only whenit exceeds the fixed costs of a peaker.2 The other key variable in thisfeedback loop is installed capacity, K. The profit function connects(short-run) profit to installed capacity.The profit function: SRB(K)In the model under consideration, demand is not elastic; price spikes are simplya matter of the price being set to the price cap whenever augmented load exceedsa certain threshold. The number of times this occurs, together with the price cap,determines the price-spike revenue. The load-duration curve is essential in makingthis determination, and it will be represented algebraically as follows:The load-duration function: D(Lg)The threshold that Lg must exceed to cause the system operator to set price tothe price cap is K!! ORR, installed capacity minus the operating reserve requirement.In the case of VOLL pricing, ORR=0, so price is set to VLL whenever Lg exceedsinstalled capacity and load must be shed. Whenever Lg>K !! ORR, then. But by the assumptions of the Simple Model of K !! Lg<ORRK !! Lg=ORReliability (Chapter 2-3), so the last inequality implies OR <ORR, or operatingreserves are less than required. This is the condition for setting price to Pcap underOpRes pricing. So, under either pricing system,Price spikes occur when: Lg>K !! ORR. The duration of their occurrence is given by D(Lg), where Lg=K!! ORR. This givesthe rule for finding price-spike duration:Price-spike duration =D(K !! ORR)Price-spike revenue is simply the duration of the price spike times the differencebetween the price cap and the variable cost of the peakers. ThusSRB(K) =D(K !! ORR) (Pcap!! VCpeak) (2-7.1)This is how to compute the profit function in the present model. Calculation wouldbe more complicated if there were a supply or demand bid above VCpeak, but theconcepts would be the same. Notice that SRB(.) is considered a function of K,although according to the right side of Equation 2-7.1 it depends on four differentvalues. Two of the other three are policy parameters, ORR and Pcap, while the last,VCpeak, is a technology parameter. Regulators (including system operators andFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-7 Market Dynamics and theProfit Function 1773. This is only strictly true when K is deterministic. The next chapter shows that when it fluctuatesrandomly, the value of OR should be a bit higher in order to induce the right average value of K.Figure 2-7.1 Profit functionsengineers) use the policy parameters, consciously or unconsciously, to control theprofit function and thereby control equilibrium installed capacity, Ke.The long-run average load-duration curve given in Chapter 2-6 isD(Lg) =.0004[.25(max(0, 52!! Lg))2+.75(max(0, 50!! Lg))2 ] (2-7.2)The constant, 3.5, used previously has been multiplied by 1'8760 so that durationis no longer given in hour/year but is simply a number, 0.0004, and thus can beused directly in Equation 2-7.1. Using this function, the profit function for bothVOLL pricing and OpRes pricing was calculated, and the results are displayed inTable 2-7.1 and graphed in Figure 2-7.1.Table 2-7.1 Profit functionsInstalledCapacity(1000 MW)KSRB(K ) in $/MWhVOLL PricingPcap=$15,000/MWhORR=0 MWOpRes PricingPcap=$484/MWhORR=5000 MW47 78.00 14.1348 42.00 11.0349 18.00 8.3250 6.00 6.0051 1.50 4.0652 0.00 2.5253 0.00 1.35

Result 2-7.1 The Higher the Price Spikes, the Steeper the Profit FunctionA pricing policy that relies on a higher, shorter-duration price spike to stimulateinvestment is characterized by a steeper profit function.2-7.2 INTERPRETING THE PROFIT FUNCTIONVOLL pricing produces a much steeper profit curve than does OpRes pricing. Thissteepness is closely related to the negative side effects discussed in the previouschapter. But the main effect of the profits described by these curves is to producethe optimal long-run equilibrium, and the two profit functions show that the twopricing policies would serve this purpose equally well.3Equilibrium. Both profit functions intersect the level of the fixed cost of a peaker,$6/MWh, when they reach an installed capacity of 50,000 MW. To the left of thisthey are greater than $6/MWh, and to the right they are less. For lower levels ofinstalled capacity, the extra profit induces investment, and for higher levels,February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.178 PART 2 PriceSpikes, Reliability, and Investmentinvestment is unprofitable and therefore will not be undertaken. Of course investorslook to the future and base their decision on estimates of expected future levelsof capacity. However, the main point remains true: Both pricing policies inducethe same equilibrium level of installed capacity, and that level can be read froma graph of the profit function.Hidden Risk. When the profit function reports a short-run profit of $6/MWh,this is not the value that will be realized in any given year but, is instead, a long-runaverage value. As explained in the previous chapter, actual profit in any given yearwill be either $0/MWh or $24/MWh under VOLL pricing and will be either$4.84/MWh or $9.48/MWh under OpRes pricing. These annual variations are notshown explicitly, yet the profit function implicitly indicates their existence andrelative magnitude.Implied Risk. Risk comes from the interaction of the unpredictability of aug-mented load with the predictable profit function. The price distribution dependson how load fluctuates relative to installed capacity. If Lg is 1% higher in a particu-lar year, it has the same effect on price as if K were 1% lower. Thus, an increasein Lg is equivalent to an equal move to the left on the profit function. If the functionis steep, the resulting increase in profit is large; if the function is relatively flat,the increase is small. Thus for a given pattern of year-to-year load fluctuations,a profit function that is 4 times steeper will produce 4 times the variability in short-run profits. Steep profit functions are inherently risky.Implied Market Power. Although market-power analysis is more complex, thesame analysis used with risk can be used to shed light on the problem of marketpower. Withholding 500 MW is equivalent to decreasing K by that amount, andthe average effect can be read from the profit function. If the function is steep,withholding is very effective at increasing profit.

Result 2-7.2 Steeper Profit Functions Increase Risk and Market PowerFor the same level of year-to-year fluctuation in the load-duration curve, a steeperprofit function will cause more variation in fixed-cost recovery and will increasethe exercise of market power.How Steep Should the Profit Function Be? The steeper the profitfunction, the greater the negative side effects, but the flatter the profitfunction, the less incentive there will be for the market to return to itsequilibrium value. Because the optimal equilibrium value is not knownwith great precision, there is nothing gained by using a profit functionthat provides extremely strong restorative forces. If the optimal K isknown to be between 48 and 52 GW with a certainty of only 50%, thereis no use in raising profit levels by $50/MWh when K is only half a GWlow. On the other hand, some slope to the profit function is absolutelynecessary.In most industries, profits 5% or 10% above the normal rate of return oninvestment are considered extremely good. A short-run profit function that paysFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-7 Market Dynamics and theProfit Function 179double the fixed costs of generating capital will yield a profit level near 10% abovenormal. An extra $6/MWh in a market with an average price of $30/MWh wouldappear to be a reasonable incentive from the perspective of both the customer andthe investor. But an excess short-profit level of $78/MWh, as is produced by VOLLpricing when K is 6% (3 GW) below optimal, seems to be more than would beneeded or could be tolerated. If this happened in a hot year, profits would betwice this high.One compromise would be to have a profit function that is steep in the vicinityof the optimal level of installed capacity, K*, but does not continue steeply oncea sufficient level of incentive is reached. This provides an incentive that becomesstrong quickly when the system deviates from optimal K* but which does notbecome excessive as K gets lower or the load-duration curve suffers a randomupward fluctuation. The next chapter shows how to design profit functions thatare steep only at the level of optimal installed capacity.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. This wind generator was constructed by Charles Brush for his personal use. The article begins by notingthat After Mr. Brush successfully accomplished practical electric illumination by means of arc lights,incandescent lighting was quickly brought forward and rapidly perfected.Theshaft is 20 feet long and 6 1'2 inches in diameter. Thewheel, which is 56 feet in diameter [is]provided with 144 blades twisted likethoseof screw propellers. Thesail surfaceis about 1,800squarefeet. Thespeed of thedynamo at full load is 500 revolutions per minute, and its normalcapacity at full load is 12,000 watts. Theworking circuit is arranged to automatically closeat75 volts and open at 70 volts. Theamount of attention required to keep it in working conditionis practically nothing. It has been in constant operation morethan two years.1Scientific AmericanDecember 20, 1890Chapter 2-8Requirements for Installed CapacityPRICE SPIKES ENCOURAGE INVESTMENT INDIRECTLY; A CAPACITYREQUIREMENT GETS RIGHT TO THE POINT. The capacity approach is definedby two regulatory parameters but, as has been demonstrated, so is the price-spikeapproach. Both can induce any desired level of reliability while preserving thecorrect mix of technology, so the choice between them should be based on theirside effects.1Chapter Summary 2-8: A capacity requirement produces an easily controlled,low-risk profit function. It can be combined with a price-spike approach to producea profit function that is still relatively low risk while providing high prices at a fewcrucial times to tap existing high-priced resources. Combining price-spike andcapacity-market profit functions does not increase equilibrium profits, but it doesincrease the equilibrium value of installed capacity unless the two policies areproperly adjusted. Adjustment requires taking account of random fluctuations inthe level of installed capacity.Section 1: The Capacity-Requirement Approach. All load-serving entitiesare required to own, or to have under contract, a certain required capacity. The sumof these is the markets installed capacity (ICap) requirement and is typically about18% greater than annual peak load. A load-serving entity is penalized if it fails tomeet its requirement.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-8 Requirements for Installed Capacity 181Section 2: Short-run Profits With a Capacity Requirement. Capacityrequirements easily induce sufficient generation by setting a penalty level that ishigher than the cost of new capacity. Random fluctuations in ICap help determinethe equilibriumlevel of ICap. This must be taken into account when designing profitfunctions which show only the deterministic equilibrium.Section 3: Combining a Capacity Requirement with a Price Spike. VOLLpricing produces an optimal average ICap level, and a capacity requirement canbe designed to do the same. If these two policies are both implemented, the resultinglevel of ICap will be too high, but this can be corrected by adjusting policy parame-ters.Section 4: Comparing the Two Approaches. Price spikes are sensitive toload fluctuations while capacity markets are not. By eliminating this source of risk,the capacity approach makes it easier to control reliability and suppress marketpower in the energy market. Price-spike systems have the advantage of sendingefficient price signals to the demand side of the market and to expensive existinggenerators. A hybrid system may be best.2-8.1 THE CAPACITY-REQUIREMENT APPROACHCapacity requirements provide a fundamentally different approach to generationadequacy. Under the price-spike approach, energy revenues cover the fixed costsof generators. Under the capacity-requirement approach, capacity revenues com-pletely cover the fixed costs of peakers and play a crucial role in determining thelevel of all types of installed generation capacity.

Result 2-8.1 Energy and Capacity Prices Together Induce InvestmentInvestment responds to expected short-run profits, which are determined byenergy prices and (if there is an installed-capacity requirement) by capacityprices. Regulatory policies determining these prices need joint consideration.Capacity requirements are a more direct approach to reliability than assigninghigh price limits when the system is short of operating reserves. This directness hasits advantages. The capacity requirement bears a relatively clear and stable relation-ship to reliability. A side effect of the capacity approach is also helpful; it eliminatesthe need for high energy price spikes to induce investment. As explained in Chapter2-6, these spikes cause investment risk and encourage market power, but the capacityapproach has drawbacks of its own.In a capacity market, demand is set by regulators who usually forget to makeit elastic; inevitably, this leads to market power. Also, defining and verifying installedcapacity is difficult. A third problem, discussed in the next chapter, occurs whenevera capacity market trades with a price-spike market.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.182 PART 2 PriceSpikes, Reliability, and Investment2. How a parameter describing consumer economics was derived fromastronomical constants remainsa mystery. Why should the cost-minimizing value of load shedding equal the time it takes the earth torotate once times the number of digits on two hands divided by the time it takes the earth to orbit the sun?How a Capacity Requirement Is ImplementedCapacity markets often serve a dual purpose. While originally derived from regula-tory requirements designed to assure adequate installed capacity, in a deregulatedenvironment they are asked to perform double duty and provide short-termreliability.This requires rules to prevent export of capacity to neighboring systems whenthese have high prices. This short-term market role and its attendant regulatorycomplications are ignored in this chapter to focus clearly on the role of capacitymarkets in securing adequate ICap. This focus is maintained by assuming the marketunder discussion is isolated and does not trade with other markets.The first step toward implementing a capacity system is to determine the optimallevel of ICap. As explained in Section 2-5.3, this can only be accomplished by tradingoff the value of lost load against the cost of more ICap. This approach is never taken.Instead the crucial input is the acceptable number of hours of load shedding, anengineering constant shrouded in secrecy but said to be one day in ten years.2 Withthis in hand and knowing the reliability of generators and the variance of load, theamount of spare capacity required to attain this level of reliability can be calculated.But often it is not calculated and a traditional value is selected. Generally therequirement for ICap is in the neighborhood of 118% of expected peak load, thoughsome systems, such as Albertas, seem to survive on considerably less. This require-ment is then divided among load-serving entities, which are retailers and regulatedutilities, in proportion to their individual expected peak loads. This produces individ-ual requirements for installed capacity.These individual requirements must be met by either purchasing generation orcontracting for its use. A contract must specify that the generator will be madeavailable to the system if requested. Any load-serving entity that fails to own orcontract for the required capacity is penalized. A second penalty applies to anygenerator that fails to perform when called on. This chapter assumes that the perfor-mance penalty is sufficiently effective so that it is rarely needed, and the penaltyfor insufficient capacity will be referred to simply as the penalty. In PJ M, thispenalty has been set at about the level of a peakers fixed cost, or about $7.38/MWh($177/MWday when adjusted for forced outages).2-8.2 SHORT-RUN PROFITS WITH A CAPACITY REQUIREMENTThe Profit Function of a Pure Capacity ApproachIf there is no market power in an isolated capacity market, the price of capacity willbe either zero or equal to the penalty. If total installed capacity, K, is less thanFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-8 Requirements for Installed Capacity 1833. If (the use of) capacity could be exported to a neighboring market, then the price of capacity wouldreflect the opportunity cost of selling into that market.Policies that Would Inducethe Same Deterministic ICapProduce Different Levels of ReliabilityRandom variations in installed capacity, K, aroundthe deterministic equilibrium, Ke, increase profitwhen the profit function is steeper on its upside.Bringing profit down to its equilibrium value requiresraising average K by an amount determined by theshape of the profit function. If two profit functions have the same Ke, the onewith the steeper upside will induce the higher aver-age K and thus more reliability at a higher cost.required capacity, KR, the price will equal the penalty, Y. If K >KR, the price shouldbe zero.3A capacity requirement is intended to induce investment when , K <KRand will be successful if Y is greater than the fixed costs of owning a newpeaker, FCpeak. As with a price-spike policy which determines a profitfunction by setting Pcap and ORR, so a capacity-requirement policy deter-mines a profit function by setting Y and KR. The profit function is the stepfunction shown at the left.Unlike the profit function for price spikes, there is no level of ICapfor which SRB(K) =FCpeak; profits are either zero or twice this value. Inspite of this, the deterministic equilibrium ICap is the required capacitylevel , but this equilibrium is maintained by small fluctuations (Ke=KR)in K that result in capacity earning the penalty price part of the time andnothing the rest of the time. This analysis depends on an understanding of K as arandom variable and a new definition of equilibrium installed capacity.Equilibrium with Capacity a Random VariablePrivate investors do not coordinate decisions to con-struct plants, and plant construction times are unpredict-able. Consequently, K will fluctuate randomly. A partic-ular profit function will lead to some particular distribu-tion of Ks, which by definition is the equilibrium distri-bution. This distribution will have some average value,Kne, called the equilibrium value of average K, or simplyaverage K. The equilibrium distribution of K will havean average profit of FCpeak just as SRB(Ke) =FCpeak. ButSRB(Kne) will not equal FCpeak, because profit functionsare usually not straight lines. This means SRB(Ke) =/SRB(Kne), so Kne does not equal Ke. The average in-stalled capacity does not equal Ke when the determinis-tic equilibrium capacity is Ke.Because Kne differs from deterministic Ke, two profit functions withthe same deterministic equilibrium may have different Knes. If a profitfunction is steeper to the left of Ke, then the equilibrium distribution ofKs must move further right to bring average profit down to FCpeak.These concepts can be applied to the profit functions of a capacitymarket. As long as such a profit function is greater than FCpeak to the leftof KR and less than FCpeak to the right, its deterministic equilibrium willbe Ke=KR. But its equilibrium-average K will differ according to theheight of the penalty. If the penalty is just slightly higher than FCpeak, thenK will need to spend much more time to the left of KR in order to bringFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.184 PART 2 PriceSpikes, Reliability, and Investment4. This assumes that the distribution of K is symmetrical.5. In real markets, there are old inefficient generators with higher marginal costs. For instance PJ Mcurrently has one with a marginal cost of about $130, so this would require a price cap of $131/MWh.6. Hobbs has proven this result in a stochastic model (Hobbs, In, and Stoft 2001).average profit up to FCpeak. Increasing the penalty moves Kne to the right and increasesreliability.Mimicking VOLL Pricing with a Capacity Requirement Suppose VOLL pricing produces a certain average installed capacity level, Kne. IfKne is also the required level (KR=Kne) under a capacity approach and the penaltyis set to $12/MWh, the same average capacity of Kne will be induced by the capacitymarket.4 In this case, price spike revenue will not be required and the price cap canbe set only $1/MWh above the peakers variable cost. This would mean a price capof $31/MWh for the two-technology model used since Chapter 2-2.5 The revenuefrom the capacity market would cover the fixed costs of peakers and would alsoflow to baseload generators thereby increasing their short-run profits by $6/MWh,just as when peakers recover their costs from energy price spikes. Consequently,baseload plants will also have an equilibrium installed capacity that is optimal. Inshort, the capacity-requirement approach can fully substitute for the price-spikeapproach with regard to inducing the optimal investment in all types of technology.6

Result 2-8.2 A Capacity Requirement Can Eliminate the Need for Price Spikes(This holds only with regard to inducing new generation, and not with regard tothe utilization of expensive demand- or supply-side resources.) In an isolatedmarket, or in a region in which all markets have adopted a capacity-requirementapproach instead of a price-spike approach, energy-price spikes are not neededto induce investment in generation. The capacity approach will induce the sameoptimal level of all generation technologies as would an optimal price-spikeapproach.2-8.3 COMBINING A CAPACITY REQUIREMENT WITH A PRICE SPIKEIf an optimal price spike approach is combined with an optimal capacity approach,the result is a market that builds too much ICap. At the optimal ICap value, genera-tors would cover their fixed-costs twice, once in the energy market and once in thecapacity market. This would encourage more investment, and ICap would rise aboveits optimal level.Profit functions for VOLL pricing and OpRes pricing, presented in Chapter 2-7,produced the same deterministic equilibrium, Ke. Consequently, both were said tobe optimal with respect to installed capacity. But the previous section argued thatthe two profit functions will not produce the same equilibrium ICap in a morerealistic model. This means that at least one of them does not induce optimal installedFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-8 Requirements for Installed Capacity 1857. This discussion assumes for simplicity that the randomdistribution of K is symmetrical. If it were not,the conclusion would still hold, although some of the details would change.capacity. Before judging the results of a combined approach, a better understandingof the VOLL pricing result is required.Interpreting Average ICap for VOLL Pricing.7Because the profit functionof VOLL pricing is very steep, Kne may be significantly greater than Ke, but wouldKne =Ke be desirable? If these were equal, there would be 1 GW too little ICap asoften as 1 GW too much. But the reliability loss from having too little is greater thanthe gain from having too much because a finite decrease in K increases blackoutsby more than the same finite increase would decrease them. Accounting for capacitycosts, this implies a greater net loss from downside errors than from upside errorsin K. It is better to have Kne somewhat above Ke.Kne is greater than Ke, but Kne should be greater than Ke. Do these two effectscoincide? Is Kne greater by the appropriate amount? In fact, it is. The long-runequilibrium condition still assures that Kne will keep price-spike revenue equal toFCpeak on average, and this means the duration of load shedding will be the optimalvalue given by Result 2-3.1. VOLL pricing produces optimal Kne even though randomfluctuations in K make this different from the deterministic equilibrium value Ke.

Result 2-8.3 VOLL Pricing Induces Optimal ICap Even When ICap Is RandomIf random fluctuations in ICap are accepted as inevitable, then VOLL pricinginduces the correct distribution of ICap. In this case, optimal average ICap willbe greater than the optimal ICap in a deterministic world with deterministic K.Combining Approaches. Because VOLL pricing is optimal, combining it withan optimal capacity approach would double the profits of generators if they main-tained the same (optimal) level of Kne. This would lead to more investment and ahigher level of ICap than justified.Because of the side effects of VOLL pricing, OpRes pricing may bea better choice for a combination. The figure to the left shows the profitfunction that would result from using both the OpRes pricing describedin the previous chapter and the capacity requirement of the previoussection. Note that the profit function still intersects that fixed-cost lineat the optimal deterministic value of ICap, 50 GW (50,000 MW).It might seem that adding the two profit functions must surely resultin too high an equilibrium ICap distribution, but that may not be the case.Profit functions that are flatter than a VOLL profit function actuallyinduce too little ICap if a deterministic analysis indicates that they areoptimal. Consequently, although combining two of them increases Kneabove the value induced by either, it may not be too high. It may be thatthe difference between Kne and Ke, even for VOLL pricing, is smaller thanthe errors in estimating Ke. In this case, the preceding analysis is not of muchimportance, except to show that combining a price-spike and capacity marketapproach should not cause too much overinvestment. Currently little is known aboutFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.186 PART 2 PriceSpikes, Reliability, and Investmentthe amplitude of the random fluctuations in K, but there is growing evidence fromthe north east of the United States that these may be large.

Result 2-8.4 Profit Functions Are Additive, but Resulting Profits Are NotCombining price spikes with an ICap market does not increase equilibriumprofits; it only induces more installed capacity.2-8.4 COMPARING THE TWO APPROACHESMarket PowerWhen K is just slightly greater than KR, the capacity market is particularly susceptibleto market power. Suppose the requirement is KR=50 GW and one supplier owns5 GW of uncommitted capacity and has no capacity requirement of its own. Alsoassume that no other supplier has any market power and that K for the entire marketis 50.1 GW. This is essentially the same situation as analyzed for the price-spikeapproaches in Section 2-6.2. Competitive bidders would bid a price of zero into a capacity market becausethere is no cost to suppling capacity. The supplier with 5 GW of capacity wouldbid just less than the penalty value, $12/MWh, because at this price it could sell 4.9GW to those with capacity requirements. This strategy raises the price on all capacityin the spot market close to the penalty price. So profits are $6/MWh greater thannormal. This may be compared with an increase in profits of $52/MWh under VOLLpricing and about $5/MWh under the example of OpRes pricing.When K<Ke, market power becomes worse under both price-spike approachesbut totally disappears under the capacity approach. Once K<Ke, the capacity marketprice is Y under competition, so market power cannot push it higher.In a capacity market, market power can be neutralized by decreasing the capacityrequirement. In this case, setting KR to 45 GW would bring the price back downto zero. If K then fell below the optimal level of 50 GW, market power would againbe exercised and the capacity price would go back up to $12/MWh. The supplierwith market power and 5 GW of capacity causes the profit function in a market withKR=45 to be exactly the desired profit function (the one that results from KR=50,and no market power).RiskAnnual changes in the load-duration function can cause dramatic year-to-yearchanges in price-spike revenues, but they cause no change in revenues from thecapacity market. After observing the 40 years of annual VOLL data displayed inFigure 2-6.1, it is impossible to decide whether expected short-run profits in the lastyear are approximately $5.40/MWh, the 40-year average, or $9.66/MWh, the averageof the last 20 years. Is it better to stay out of the market or is it a very profitable timeFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-8 Requirements for Installed Capacity 187to invest? This source of uncertainty is entirely absent from markets using thecapacity approach.Investing in markets that are based on a pure capacity-requirement approach isstill risky because profits depend on how much other capacity enters the market.But unless the market is grossly overbuilt, demand growth should restore theequilibrium fairly soon. Investors do not need to wait until a favorable combinationof low K and exceptionally high load produces a super profitable year, making upfor all the years of low profits.Demand ResponseThe weakness of a pure capacity-requirement system is that it produces no pricespikes. These are needed to take advantage of demand elasticity and are also neededto stimulate the development of that demand elasticity. Price spikes are also neededto make use of old inefficient generators and the emergency output of other genera-tors. A hybrid system can accomplish this while minimizing risk and market power.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. Cournot anticipated J evons, Menger, and Walras in discovering the law of one price and otherneoclassical results. J evons (1835-1882), with his publication of The Coal Question in 1865, was the firstto draw attention to the imminent exhaustion of energy supplies. In 1870 he invented the logical piano,the first machine to solve problems faster than a human.In thesameopen market, at any moment, therecannot betwo prices for thesamekind of article.W. Stanley Jevons TheTheory of Political Economy1879Therearetwo fools in every market; oneasks too little, oneasks too much. Russian proverbChapter 2-9Inter-System Competition for ReliabilityMARKETS WITH LOW PRICE CAPS HAVE LITTLE PROTECTION FROMCOMPETING MARKETS WITH HIGH PRICE CAPS. At crucial times, the high-cap market will buy up the reserves of the low-cap market. This can cause a groupof competing markets to evolve toward a risky high-priced regulatory approach.Competing systemoperators are not led by an invisible hand to the optimal policy.This chapter uses previously developed models and tools to investigate whathappens when pairs of markets, operating under different pricing rules, competefor energy and capacity.1Chapter Summary 2-9: Competition between markets with different price capswill favor the market with the higher cap. The lower-price-cap market will spendas much on inducing investment but will find its reserves bought out from underit at crucial times by the high-price-spike market. The result will be competitionbetween system operators for the higher price cap unless a regional regulatorprevents this. Capacity-requirement markets can solve a similar problem by requir-ing capacity rights to be sold on an annual basis.Section 1: Price-Cap Competition. A VOLL market and OpRes market,identical except for their pricing policies, are modeled as able to trade energy andoperating reserves. The result is that when load is expected to be high, moregenerators sell power and reserves to the VOLL market. This equalizes the expectedshort-run profits in the two markets; as a result the OpRes market suffers reducedreliability. This will force it to adopt a higher price cap to protect itself from inter-system competition.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-9 Inter-System Competition for Reliability 1892. Obviously, seasonal variations in load are much greater, but they are partially offset by seasonalvariations in planned outages. The real effects described here may be much larger than depicted in theseexamples which are intended only for qualitative analysis.Section 2: Competition between Price Spikes and Capacity Require-ments. Pure capacity-requirement markets will suffer the same fate as OpResmarkets unless they make their capacity requirement annual. This will protect them,even from VOLL markets.2-9.1 PRICE-CAP COMPETITIONChapter 2-6 developed models of VOLL pricing and OpRes pricing that made useof common supply and demand conditions. Chapter 2-7 extended the analysis byconstructing profit functions for the two markets. This section considers what wouldhappen if two of these markets, one VOLL market and one OpRes market, weretrading partners but were isolated from all other markets.Each market has its own system operator which must serve a load describedby the load-duration curve of Equation 2-7.2. This is a long-run average curve, andit summarizes many fluctuations in load, both predictable and unpredictable. Thissection is concerned with predictable fluctuations, such as seasonal ones. For easyreference call the high load season summer and call the non-summer winter. Forsimplicity, assume that these seasons shift the load duration curve uniformly. Inthis case they are equivalent to an equal but opposite shift in installed capacity,K.Because (augmented) load minus installed capacity (Lg! !K) determines short-runprofits, the new profit function during a season is found by shifting the averageprofit function to the right in the summer and the left in the winter. Assuming forsimplicity that K is deterministic, the optimal ICap level in each market is 50 GWas explained in Chapter 2-6. As a benchmark, assume that the two markets eachstart out with this level of capacity, and consider the case, shown in Figure 2-9.1,in which load is 1 GW above normal in the summer and 1 GW below normal inthe winter.2 Installed capacity does not change by season and is always 50 GW ineach market, but profits are high in the summer and low in the winter as depicted.Trade between the two markets will produce different equilibria in the summerand winter. Assuming the interconnection allows sufficient trade, these equilibriawill have two defining characteristics:1. Profits in the VOLL and OpRes markets are equal.2. The average capacity sold to the two markets is 50 GW.If the OpRes market were more profitable, some generation would migrate fromthe VOLL market to the OpRes market and equalize the profit levels. Then themigration would stop. Equilibriumoccurs when profits in the two markets are equaland one market is short as much generation as the other is long. The allocation ofgeneration between the two markets is shown by the dots in Figure 2-9.1. In thesummer the average short-run profit of a peaker will be about $9.60 and the VOLLmarket will have about 1250 MW more generation under contract than the OpResmarket. In the winter the OpRes market gets more and the price is about $3.30.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.190 PART 2 PriceSpikes, Reliability, and InvestmentFigure 2-9.1VOLL and OpRes profitfunctions for high- andlow-load conditions. (Note that these are notthe standard, long-runaverage profit functions,but they do average loadfluctuations over twodifferent seasons.)This is a good deal for the VOLL market. As an isolated market it would havehad to pay enough for reserves to provide profits of $18/MWh and would havehad fewer reserves in crucial hours. Reliability would have been less. More detailedcalculations confirm that even when the winter is taken into account, the VOLLmarket has increased reliability at a reduced cost, while the OpRes market hasreduced reliability at an increased price.Trade between markets essentially lets the high-spike market steal the reservesof the low-spike market. They pay the same price for reserves, but the high-spikemarket gets them when they are needed and the low-spike market gets them whenthey are not. Moreover, because they are not shared evenly, they are less effectiveat preventing blackouts than if they were, so the overall reliability of the marketis reduced.The result will be that low-spike markets are forced to adopt higher price caps.This competition between system operators leads to the adoption of regulatorypolicies that favor risk and market power. When inter-system competition is ignoredand different markets are allowed to adopt different policies, the result is high-pricespikes even if all would prefer low price spikes. Each one finds it advantageousto outbid its neighbor and will do so when desperate, at first in secret out-of-market purchases and the later by raising price caps. Only through explicit high-level regulation can a low-risk policy be implemented.

Result 2-9.1 Competition Between System Operators Induces High Price SpikesIf two markets with different price spike policies trade energy and operatingreserves, the one with higher price spikes will gain in reliability and save moneyrelative to the other. This will force the low-spike market to use higher pricespikes. If regional price limits are not imposed, inter-system competition will leadto reliability policies with undesirable side effects.Further analysis reveals that summer must have a duration of 25% and winterof 75%, the resulting profit level for peakers in only about $5/MWh, less than the$6/MWh required for equilibrium. This means that competition between the marketswill cause a decrease in investment, and there will be less than the optimal levelFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-9 Inter-System Competition for Reliability 1913. With two markets trading, each would require a lower level of installed capacity because they couldshare resources. This is one of the main reasons tie lines have been built historically. But this model doesnot account for emergency sharing. Each market must serve its own load once generators have signedcontracts with one or the other. Emergency sharing is not allowed. Within this model, bringing the twosystems into trading contact would produce a lower equilibriumlevel of ICap and less reliability. A morecomplex model that allowed emergency sharing would have a reduced optimal level of ICap, but it toowould demonstrate that the combined systemwould produce too little reliability.of installed capacity. Total reliability will decline both because total installedcapacity declines and because it is not distributed optimally between the twomarkets.3

Result 2-9.2 Trade between Markets with Different Policies Can Reduce ReliabilityWhen two markets that trade with each other implement different price caps thatwould provide optimal reliability if implemented in an isolated market or by allmarkets, the outcome will usually be suboptimal. Trade will reduce averageprofits in both markets and leave too little incentive for investment. 2-9.2 COMPETITION BETWEEN PRICE SPIKES AND CAPACITY REQUIREMENTSMarkets with a capacity requirement will typically contain a submarket (or severalsubmarkets) for trading the capacity that load-serving entities must contract forto satisfy their capacity requirements. The term capacity-requirement marketwill not be used to refer to these submarkets but rather to the entire power marketthat relies on a capacity requirement to induce a reliable level of investment ininstalled capacity. The term capacity-requirement market is analogous to the termsVOLL market and OpRes market. Each of these markets also has its own pricinglimits for the system operator. VOLL markets have extremely high pricing limits,OpRes markets have lower limits, and capacity-requirement markets have the lowestlimits because they do not need a price spike to cover the fixed costs of peakers.Capacity markets can suffer a fate similar to the fate of low-price-cap markets.If capacity requirements are enforced on a daily basis, then on a day when the price-spike market expects a price of $600/MWh, the $12/MWh penalty of the capacitymarket loses its sting. A load-serving entity will offer a generator $11.99/MWhfor its capacity and the generator will decide instead to accept $600/MWh for itsenergy from the market next door.The situation is more complicated in real markets because capacity requirementsare inevitably accompanied by energy price spikes, and the markets have complexrules allowing the export of energy from capacity under contract as well as its recallwhen needed. Nonetheless, on days when the capacity market is likely to be shortof energy so recall of capacity is likely, a higher expected energy price in exportmarkets can easily overcome a modest capacity penalty. This allows the same typeof reserve stealing described in the previous section.The root of this problem is the predictable fluctuations in load that produce thehigh-load periods and low-load periods described above. So long as these exist,the high-price-spike market will win the reserves at times when it pays most toFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.192 PART 2 PriceSpikes, Reliability, and InvestmentFigure 2-9.2VOLL and OpRes profitfunctions for high andlow load conditions.win. A capacity market can solve this problem by annualizing its penalty so thatgenerators must sell their capacity for a year at a time. Then the generators choiceis between a year of revenues from the capacity market and a year of revenues fromthe external market. In this case there is no possibility of participating in the price-spike market when load is high and in the capacity market when load is low. Asin the previous section, this assumes generators must sell into one market or theother, a convenient simplification.

Result 2-9.3 Capacity-Requirement Markets Need Annual RequirementsCapacity markets are vulnerable to competition from price-spike markets unlessthey utilize an annual requirement.A Model with Annual Requirements. Assume again that there are two marketswith a strong tie line connecting them and allowing a considerable amount of trade.One is a VOLL market, and the other a pure capacity-requirement market. Thecapacity-requirement market, because it has no price-spike incentive, has a penaltyof $12/MWh, twice the fixed costs of a peaker. It also has an annual requirementfor installed capacity.Analysis. Figure 2-9.2 shows the profit functions for the two markets. If bothmarkets had 50 GW of capacity, they would share it equally. If the capacity marketgot any less, its price would be $12/MWh and the VOLL markets expected pricespike would be slightly less than $6/MWh. This would attract capacity back to thecapacity market.The pairs of horizontally connected dots show how capacity would be dividedbetween the two markets if the total capacity in the two markets differed from theequilibrium level of 100 GW. If there were 101 GW, the VOLL market would getthe extra GW of capacity, and the price in the capacity market would sink to$1.50/MWhthe opportunity cost of not selling into the VOLL market. If therewere slightly less than 100 GW, the capacity-market price would rise to $9/MWhand it would still retain its full 50 GW required capacity. The VOLL market wouldabsorb the shortage.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-9 Inter-System Competition for Reliability 193Figure 2-9.3VOLL and capacity-market profit functionsfor high and low loadconditions.Once capacity was more than about 0.5 GW short, the capacity-market pricewould rise to its penalty level of $12/MWh and beyond this point it would absorbany further decrease in combined capacity. This should not prove too problematicbecause whenever capacity is short in the combined system, price rises above thefixed costs of a peaker quite quickly and this should induce investment.Unlike the two markets in the previous section, neither market has a strongadvantage over the other. They compete on an annual basis so the VOLL marketcannot buy up reserves only at the times they are most needed.Shorter-Term Capacity Requirements. If the capacity requirement can bemet for less than a year at a time, say for three months, then it will have to competewith the VOLL market during high-load and low-load seasons. This is shown inFigure 2-9.3. J ust as in Section 2-9.1, the VOLL market wins out during the high-load period. It gets more of the reserves and has a lower price spike than it wouldotherwise have. It suffers no penalty during the low-load period when both marketsfare exactly as they would have if they had not been in contact.Complications. Capacity markets can protect themselves in other ways fromexternal price spikes, so they may not need to use an annual requirement. PJ Ms$1,000/MWh price cap plus its ability to pay higher prices in out-of-markettransactions offers significant protection, although it does bring with it the standardside effects of price spikes.The present examples all consider two markets that are the same size. If theprice spike market is bigger, then it will buy up more of the other markets capacity.Small low-spike markets and small capacity-requirement markets are more at riskthan large ones.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Theday when weshall know exactly what electricity is, will chroniclean event probablygreater, moreimportant than any other recorded in thehistory of thehuman race. Thetimewillcomewhen thecomfort, thevery existence, perhaps, of man will depend upon that wonderfulagent.Nikola Teslac. 1893Chapter 2-10Unsolved ProblemsLOW PRICES, EVEN THOSE ONLY 200% ABOVE NORMAL, CAN INDUCEINVESTMENT, BUT THEY CANNOT INDUCE CURTAILMENT OF HIGH-VALUE LOAD. Neither can they induce supply from the odd high-marginal-costgenerator nor from a generator that is producing in its emergency operating range.The problems of low price caps have nothing to do with adequate investment ingenerating capacity. They concern only the short-run responses of high-value loadand high-marginal-cost supply. These problems are small compared with theproblem of long-term market stability and generation adequacy, but they are worthsolving. This chapter defines them and suggests steps toward solutions.Chapter Summary 2-10: Genuinely high-marginal-cost power should bepurchased in a market separate from the regular supply market and with its ownhigh price cap. Load reductions, most of which have high marginal values, shouldbe purchased at a price that is allowed to exceed the price cap in the supply market.The (relatively) low price cap of the supply market should be set regionally andenforced strictly to prevent out-of-market purchases.Section 1: High Marginal Costs and Low Price Caps. Several small sourcesof high-marginal-cost power make high prices worthwhile. To avoid disruptiveside effects, these should be restricted to an emergency power market that catersonly to high-cost sources. The problem is to select only these sources and limitmarket power under a high price cap. An adequate solution appears to be withinreach.Section 2: Pricing Supply and Demand Separately. Allowing demand-sideprices to rise above the supply-side cap makes use of existing demand responsive-ness and stimulates the development of greater elasticity. This requires a methodof setting price higher than any supply bid and of refunding the extra revenuecollected.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-10 Unsolved Problems 1951. This is not the type of price cap used in other markets but is instead a purchase-price limit on thesystemoperator as explained in Chapter 2-4.Section 3: Price-Elastic Demand for Operating Reserves. An additionalmegawatt of operating reserves is worth more when reserves are near zero thanwhen they are near the required level. The demand for reserves should be expressedby an elastic demand function. Estimating an optimal function may be quitedifficult, but improving on current practice should not be. Section 4: System Operators Psychology. Some argue that systemoperatorsfind it impossible to respect a price cap, especially a low one, when operatingreserves are in short supply. If this is true, low price caps would always be under-mined by out-of-market purchases at prices above the cap. The problem is morepolitical than economic or psychological. A hard, interconnection-wide cap isrequired to solve the problem, and this can be implemented only by the highest-levelregulatory authorities.2-10.1 HIGH MARGINAL COSTS AND LOW PRICE CAPS1Sometimes particularly low price caps are desirable because of problems with eithermarket power or scarcity rents. This complicates the price-cap design, but evenquite high price caps need exceptions for peculiar generators.There are three classes of exceptions: (1) expensive generators that have notbeen built (e.g., backup generators); (2) expensive existing generators (e.g., oldgenerators); and (3) the expensive emergency output levels of cheap generators.These exceptions are small, perhaps 5% capacity, and represent extremely littleenergy. Emergency output from baseload and midload generation is the mostimportant of the exceptions and perhaps the most difficult to accommodate.Approximately 3% of PJ Ms total installed capacity is classified by generationowners as being in the emergency operating range. Some of this should becomeavailable at a price above the generators typical variable cost but below a typicalOpRes price limit of $250 to $1000/MWh, but some emergency output capabilitymay still be unreported, so the full extent of this problem is still unknown.Price caps below the variable cost of new peaker technology should be avoided.If such a low cap is needed, the market should be re-regulated. Other price-capdiscrepancies could be handled by a separate market for emergency power.An Emergency Power Market. Only capacity accepted into the emergencypower market would be paid the potentially high prices in that market which wouldbe capped at a higher level than the regular spot market. The design problem isto find a way to accept all high-marginal-cost capacity without accepting muchlow-marginal-cost capacity and to contain market power in the emergency powermarket. (In a well-functioning market, such price discrimination would be anexercise of monopsony power, but as explained in the preceding chapters, theseFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.196 PART 2 PriceSpikes, Reliability, and Investmentprice limits are explicitly designed to cover fixed costs with optimal installedcapacity.)Rules for Acceptance. Generators should self-select into the emergency marketsubject to certain limitations, which might include any of the following: the percentof the emergency markets capacity controlled by one entity could be limited; thefrequency of entering and leaving could be limited so they cannot just enter when-ever hot weather is predicted; or the percentage of emergency capacity acceptedfrom a standard generator could be limited.The last limitation is perhaps the most important. Emergency capacity mightbe defined as capacity beyond the maximum output observed while price was underthe regular markets price cap during the last year. This might need to be correctedfor ambient temperature or other factors.Bid Limitations. This market should be capped at no more than VLL, with thelevel set to make the proper trade-off between market power and inducement ofsupply. Requiring longer duration bids should reduce the exercise of market power.If market power is only a small problem, bids may be superfluous, and the systemoperator can just set prices and let supply respond, in the way load may respondto a high price.Extent and Effect of Market Power. Any proposed design should be analyzedfor market power as the emergency market will be quite susceptible to it. In doingso, it should be remembered that, once load has been shed, having the energy attoo high a price (but still below VLL) is better than not having it at all. Prognosis. A useable design should not be difficult to discover. For a low butplausible price cap on the non-emergency market, consider a $250 price cap in PJM.The amount of generation with marginal cost above this level is quite small, perhapswell under 5%. It should be possible to include most of this in the emergencymarket, and at worst it should all become available by the time the emergency pricereaches some high cap, say $10,000. While significant market power might beexercised in this market, as long as the system operator offers to pay no more thanthe power is worth, consumers will be better off with than without the market.Consider a generator that can produce 500 MW with a marginal cost of$25/MWh, an additional 5 MW with marginal costs up to $250/MWh, and another5 MW with marginal costs up to $2,000/MWh. Observing past behavior revealsthat 505 MW are available at a price of $250/MWh or below, and so only capacitybeyond this level is allowed into the emergency market. Assume that market poweris exercised by another supplier and the emergency market is called into play ata price of $3,000/MWh. The generator in question will profit handsomely fromthe exercise of market power (not its own), but consumers will benefit from theextra 5 MW of emergency power if this is used during a period of load sheddingwhen that power is worth, say, $15,000/MWh. Without the emergency market, thispower would have been withheld, exacerbating the market power already exercised.In summary, the emergency market allows the system operator to make use ofhigh price spikes without suffering the significant side effects caused by high pricespikes applied to the entire spot market. Though the potential for increased effi-February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-10 Unsolved Problems 197ciency is clear, the magnitude of this gain is not. Because emergency power is onlyneeded for a few hours per year and constitutes only a few percent of total power,gains are limited. Although this power can be very valuable, it will also be verycostly. A quantitative evaluation of potential efficiency gains is needed.2-10.2 PRICING SUPPLY AND DEMAND SEPARATELYLow price spikes can call forth any level of investment, but they cannot make useof high-cost generation or high-value load. An emergency power market could takecare of the supply side, but the demand side might also operate more efficientlywith higher prices. One possibility is to set demand-side prices higher than supplyprices during price spikes. This would require a balancing account to keep the tworevenue streams equal in the long run.Most load, like most generation, will be hedged by long-termcontracts, but somewill be subject to spot-market prices. This load should consist of customers whocan buy power more cheaply by accepting the spot price and adjusting their usageto price, thereby taking advantage of cheaper off-peak power. Faced with a volatilespot market, load-serving entities may find it advantageous to encourage demandresponsiveness from their customers. They could offer prices which hedge custom-ers yet let them save money by responding to real-time prices. Such pricing wouldensure that if their load-profile is no more costly than the average load profile theywill pay no more than fully hedged customers. In short, a more volatile spot marketfor demand can encourage a greater demand response immediately and improvedemand responsiveness in the long run.Allowing the demand-side price to exceed the supply-side price means morerevenue will be collected than dispersedthe system operator will make a profit.This is not different, except in sign, from the fact that the system operator normallyruns a deficit. To compensate, extra costs beyond the cost of energy, such as thefixed cost of wires, are typically collected through an uplift spread over all loadon a per-MWh basis. Extra revenues could be returned the same way. In fact theywould tend to cancel the uplift and remove a small taxation inefficiency.The major unsolved problems associated with this proposal seem political, butthe uplift adjustment should be examined carefully and the rules for setting thedemand-side price in the absence of demand-side bids deserve attention. The nextsection addresses this problem.2-10.3 PRICE-ELASTIC DEMAND FOR OPERATING RESERVESThe current pricing of operating reserves is black or white. If reserves are at allshort (OR less than required OR) then the market price is set at the price capatleast in theory. If OR >ORR, then extra operating reserves are priced at zero. If therule is followed in a competitive market such as PJMs, the result is an energy priceof no more than $150 when the market has 1 extra MW of operating reserves anda price of $1,000 when the market has 1 MW too few. (There are indications fromFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.198 PART 2 PriceSpikes, Reliability, and Investmentseveral markets that systemoperators realize this does not make sense and introducesome price elasticity for reserves on an ad hoc basis.)There are engineering fables about the risk of blackout taking a sudden jumpup when the level of reserves falls below the amount of supply that could be lostby the single largest outage (the single-contingency rule). These are never supportedby probabilistic calculation and are seen to be implausible when a few realisticmitigating factors are considered. First if the system is 10% short of 10-minutespinning reserves, this may simply mean that this systemwill lean on the intercon-nection for 11 minutes instead of 10. This depends on the details of the availablespin. Next there is the possibility of voltage reductions, again an uncertain value.Spinning reserve may prove to be noticeably different from its nominal value asmay nonspinning reserve. The list goes on. The probability of lost load does notchange abruptly with a 1 MW change in operating reserves.As a consequence, the value of operating reserves changes smoothly, a fact thatshould be reflected in the system operators willingness to pay for them. If 4 GWof operating reserves are required, and if operating reserves have a marginal valueof $1,000/MWh when only 3.9 GW have been purchased, then even with 5 GWon hand they probably have a marginal value of at least $500/MWh. With only1 GW of supply, their marginal value must be much greater than $1,000/MWh.

Result 2-10.1 The Price of Operating Reserves Should Increase When They Are ScarceThe view that an additional MW of operating reserves is worth any price whenthey are in short supply and worth nothing when they exceed the required levelis inappropriate in a market setting. Like every other demand curve, the demandfor reserves should be downward sloping.This should be reflected in an explicit, downward-sloping demand function foroperating reserves spanning a range of perhaps 15% of load. The first benefit wouldbe an increased elasticity of demand and a reduction of market power. Second,it would provide a way to set price at times when the supply-side price is at its cap.This would greatly facilitate separate demand-side pricing.The unsolved problem is how to determine the (elastic) demand function foroperating reserves. Valuing them requires a combination of engineering andeconomics. Their value might be determined from the impact of a 1 MW increaseon the expected amount of lost load. But if Assumption 2-3.1 (the basis of theSimple Model of Reliability) is correct, this approach may not make sense. Insteadit may be necessary to value operating reserves by a method that explicitly accountsfor the demand response to the market prices set by reserve pricing or to reductionsin market power from operating-reserve demand elasticity.2-10.4 THE PSYCHOLOGY OF SYSTEM-OPERATORSOne objection to price caps, especially to low price caps, is that system operatorsfind adhering to them psychologically difficult. They are used to doing all they canto maintain reliability. When reserves are low, they may not be able to resist theFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 2-10 Unsolved Problems 199temptation to pay more than the price cap in out-of-market purchases. As evidencefor this view, out-of-market transactions by the California and PJ M ISOs are oftencited.While there is some truth to this view, the out-of-market purchases have otherexplanations. First, they were required and successful. They were required becausethere was no regional price cap in effect, and the ISOs were subject to the type ofinter-system competition described in Chapter 2-9. This causes a loss of reliabilityfor the system that has the lower price cap. Reliability can be improved by out-of-market operations which in effect raise the low price cap. Second, the ISO rulesclearly allowed such breaches of the price cap. Failing to take advantage of thispossibility might have brought a reprimand had the system suffered a rotatingblackout.A hard, regional price limit is needed, preferably one that has been implementedby the highest authority. All system operators should be forbidden from using out-of-market operations. This does not preclude the existence of an emergency marketwith restricted participation.Assume such a price cap has been implemented, and examine the situation fromthe systemoperators viewpoint. Say reserves are tight and the market price is equalto the price cap. Also assume that the price cap is above the marginal cost of anygenerator, exceptional generation having been removed to the emergency market.If generators believe the price cap will hold, no generator will withhold outputbecause this can only reduce its profits.Suppose one generator tried to break through the price cap by approaching thesystem operator in private with an offer to supply an additional 100 MW of powerat a price of $100/MWh more than the cap. This is tempting to the system operatorwho needs more power. It may even be forced to shed load without this power.Certainly it is worth the price being asked, which is well below the value of lostload. What should the operator do? It may be a psychologically difficult decision,but it is logically simple.By accepting the offer, the operator would ensure that the generator would beback next time withholding more and asking a higher price. Moreover, othergenerators would soon learn to play the same game. By giving in, the systemoperator encourages more withholding and increases the cost of power. If the systemoperator continues to accept such offers, the requested price will eventually beraised to an unaffordable level. Some negotiations will end with a high price beingpaid, but some will end in stalemate with generators withholding capacity to provetheir threat is credible. Reliability will suffer. Surely, system operators will under-stand this and hold firm, especially when breaking the price cap leaves themvulnerable to charges of misconduct.If system operators hold fast, they have every prospect of soon being free fromsuch difficult situations. Refusing to pay prices above the cap puts the generatorin a very difficult situation. First, withholding capacity with price at the cap reducesits profits. Second, as an attempt to exercise market power, it is a violation of theFederal Power Act. If the generator actually does withhold, it does so underemergency conditions and may even cause a blackout. Moreover, the only motivefor withholding power once the system operator rejects the offer is to cause a powerFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.200 PART 2 PriceSpikes, Reliability, and Investment2. PJ M does not release information on out-of-market prices.shortage. It cannot be explained by normal profit maximization of the type thatexplains market power because the generator has actually reduced its profits.Given these considerations, it seems reasonable to expect that system operatorswill overcome any predisposition to violate the price cap. They need only thinkahead and realize that maintaining the price cap will, in the not-to-distant future,increase reliability, hold down costs, and prevent ever more difficult dilemmas.The unsolved problem is how to bring about a hard, regional price cap. Thisis a political, not an economic, problem. It is made all the more difficult becausethe relevant region is the entire interconnection. Until this problemis solved, systemoperators will continue to make secret out-of-market purchases in order to protecttheir systems from the high price caps and secret purchases by competing markets.2February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Part 3Market Architecture1 Introduction2 The Two-Settlement System3 Standard Market Designs4 Ancillary Services5 The Day-Ahead Market in Theory6 The Real-Time Market in Theory7 The Day-Ahead Market in Practice8 The Real-Time Market in Practice9 The New Unit-Commitment Problem10 A Market for Operating ReservesFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Theconclusion seventeen years later, is essentially thesame. . . industries differ onefrom theother, and theoptimal mix of institutional arrangements for any oneof them cannot bedecidedon the basis of ideology alone. Thecentral institutional issueof public utility regulationremains . . . finding thebest possiblemix of inevitably imperfect regulation and inevitablyimperfect competition. Alfred E. KahnTheEconomics of Regulation1995Chapter 3-1IntroductionREAL-TIME TRANSACTIONS REQUIRE CENTRAL COORDINATION;WEEK-AHEAD TRADES DO NOT. Somewhere in between are dividing lines thatdescribe the system operators diminishing role in forward markets. Where to drawthose lines is the central controversy of power-market design. A related controversy,not considered in Part 3, is how finely the system operator should define locationalprices. Those who favor a large role for the system operator in one sphere tend tofavor it in others. Thus the controversies of market architecture have a certainconsistency. Although the rhetoric focuses on how centralized a design is, the litmustest in most of the controversies is the extent of the system operators role. Thistoo may be a distraction. A larger role for the system operator implies a smallerrole for profitable enterprises. One side fears the inefficiency and market-powerabuses of private parties playing social roles. The other side fears the inefficiencyof nonprofit organizations but also covets the central market roles played by thesystem operator. Power markets present unusually acute coordination problems. They are theonly markets that can suffer a catastrophic instability that develops in less than asecond and involves hundreds of private parties interacting through a shared facility.The extent and speed of the required coordination are unparalleled. Generators2000 miles apart must be kept synchronized to within a hundredth of a second.Such considerations require a market that in some respects is tightly controlled inreal time. Historically, this control has extended to areas far from the precariousreal-time interactions. As deregulation brings markets into new areas, it is notsurprising to find the proponents of markets reaching beyond their ability and tofind the traditional system-control structure attempting to perpetuate now unneces-sary roles for itself. This clash of interests has produced much heat and shed littlelight.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-1 Introduction 203While Part 2 ignores questions of architecture to focus on structure, Part 3considers alternative designs for the real-time (RT) market and the day-ahead (DA)market, as well as the relationship between the two. Most of the design questionsrevolve around the extent of the system operators role.Chapter Summary 3-1: After preliminary definitions of forward, future, real-time, and spot markets, this chapter outlines the controversies over bilateral markets,power exchanges, and power pools. Bilateral markets provide a private coordinatingmechanism; exchanges provide a public, centrally determined, market price; andpools provide a price, side payments and instructions on which generators shouldstart up. The final section provides a brief introduction to locational prices, thecomplexity of which plays a role in assessing the need for central coordination.Section 1: Spot Markets, Forward Markets, and Settlements. Forwardmarkets are financial markets, while the RT market is a physical market. To theextent power sold in the DA market is not provided by the seller, the seller mustbuy replacement power in the spot market.Section 2: Architectural Controversies. The most basic controversy is overthe use of a bilateral DA market as opposed to a centralized market run by thesystem operator. If the DA market is centralized, the second controversy is overthe use of a power exchange with a single price and simple bids as opposed to apower pool with multipart bids and make-whole side payments. Multipart bidsare used to solve the unit-commitment problem, that is, to decide which generatorsto commit (start up). This problemand the problem of dispatching around congestedtransmission lines are the two technical problems that underlie the controversies.Section 3: Simplified Locational Pricing. All markets discussed in Part 3produce energy prices that are locationally differentiated, but the theory of suchprices is not presented until Part 5. The key properties of these prices are (1) theyare competitive prices, (2) the locational energy-price difference is the price oftransmission, and (3) a single congested line makes the price of energy differentat every location. Because they are competitive prices, any perfectly competitivemarket, whether centralized or bilateral, will determine the same locational prices.3-1.1 SPOT MARKETS, FORWARD MARKETS AND SETTLEMENTSTrading for the power delivered in any particular minute begins years in advanceand continues until real time, the actual time at which the power flows out of agenerator and into a load. This is accomplished by a sequence of overlappingmarkets, the earliest of which are forward markets that trade nonstandard, long-term,forward contracts. Futures contracts are standardized, exchange-traded, forwardFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.204 PART 3 Market Architecturecontracts. Electricity futures typically cover a month of power delivered duringon-peak hours and are sold up to a year or two in advance. Most informal forwardtrading stops about one day prior to real time. At that point, the system operatorholds its DA market. This is often followed by an hour-ahead market and an RTmarket also conducted by the system operator. All of these markets except the RTmarket will be classified as forward markets.All except the RT market are financial markets in the sense that the deliveryof power is optional and the sellers only real obligation is financial. If power isnot delivered, the supplier must purchase replacement power or pay liquidateddamages. In many forward markets, including many DA markets, traders need notown a generator to sell power. The RT market is a physical market, as all tradescorrespond to actual power flows. While the term spot market is often used toinclude the DA and hour-ahead markets, this book will use it to mean only the RTmarket. A customer who buys power in a forward market will receive eitherelectricity delivered by the seller or financial compensation. This financial compen-sation is called liquidated damages, meaning the damage to the customer has beenexpressed as a liquid, financial sum. Because customers are virtually never discon-nected when their forward contract falls through, power is delivered and they arecharged for it. This cost defines the liquidated damages. In most cases, a seller whocannot deliver power from its own generator will purchase replacement power forits customer. In either case the obligation has been met financially.The most formal arrangement for purchasing replacement power occurs in thesystem operators markets. Any power that is sold in the DA market but notdelivered in real time is deemed to be purchased in real time at the spot price ofenergy. This is called a two-settlement system and has a number of useful economicproperties which are discussed in Chapter 3-2.3-1.2 ARCHITECTURAL CONTROVERSIESThree architectural controversies have plagued the design of power markets. Allthree surfaced early and remain in dispute. Each has a decentralized side (listedfirst) and a centralized side. These are:1. Bilateral markets vs. centralized exchanges and pools.2. Exchanges vs. pools.3. Zonal pricing vs. nodal pricing.Because the controversies have often been seen in ideological terms, discussionhas been characterized by black and white assertions. In reality, there are manytrade-offs and only a few clear-cut answers. Part 3 does not address the third controversy; it is listed for completeness. Butall of the markets discussed in Part 3 are assumed to take place in the context oflocational pricing, so nodal pricing, or something similar, must be imagined in thebackground. The complexity of locational pricing figures in the discussion of marketcentralization. The first two controversies are addressed repeatedly as differenttime frames and different problems are considered.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-1 Introduction 205Two technical complexities and one problematic simplicity underlie thesecontroversies. The complexities are (1) transmission limits, and (2) the nonconvexstructure of generation costs. The first interacts with the physical laws of powerflow to produce different costs of delivered power at every point in the systemwheneven a single line restricts trade. This drives the third controversy, but it also playsan important role in the first. Can a decentralized bilateral market solve the problemof optimizing power flow over a grid in which every trade affects the flow of poweron every line?The second complexity, referred to as the unit-commitment problem, alsoinvolves a simultaneous optimization over all of the markets generators. Startupis costly, and the value of committing (starting) a unit of generation depends onthe cost of power produced by many other generators. Some believe a power poolis needed to collect all the relevant data and make a centralized calculation in orderto determine if the value of starting is worth the cost. Others say a power exchangeprovides enough centralization by computing a public market-clearing price.Suppliers can use this to solve their own unit-commitment problems individually.The problematic simplicity is the nature of AC power flow. This is most easilyunderstood by considering the grid at a time when line limits play no role; thenthe power grid is like a pool of water. Any generator can put power in and any loadcan take it out; no one knows where their power goes or where it comes from. Froma physical perspective it does not matter. But this makes normal private tradingarrangements impossible. Unless there is a centralized accounting of all trades,any load or generator can steal power from the pool with impunity.Bilateral vs. Central Markets. The first two controversies concern the role ofthe system operator, which some wish to minimize on general principles. Chapter3-4 considers the ancillary services that the system operator must either provideor make sure are provided by appropriate markets. While bilateral markets arereasonably efficient at providing the main service, bulk power supply, Chapter 3-6argues that they are too slow to provide efficiently the two ancillary services mostcrucial to reliability: RT balancing and transmission security. Chapter 3-5 considers centralization of the DA market and finds the answeris less obvious. With more time for trading, the slower bilateral design mightperform well enough, but the unit-commitment problem and the need for coordina-tion with regard to transmission limits tip the balance. Though it may not beessential, there is a strong case for at least the minimal central coordination providedby a power exchange run by the system operator.The decisive factor in all of these decisions is the need for speed. Bilateralmarkets are slower than centralized markets. Because of the extreme complexityof solving the unit-commitment problem and transmission problemsimultaneously,a bilateral market is simply too slow. They are slow mainly because they lack atransparent market price. Price is the coordinating agent of free markets, andbilateral markets make it difficult to discover while centralized markets make iteasy. By providing a transparent price, a centralized exchange makes finding anefficient set of trades much easier and much faster. In power markets, that meansa great deal.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.206 PART 3 Market ArchitecturePower Exchanges vs. PoolsPools are often associated with nodal pricing andexchanges are sometimes thought to require asingle price throughout their region. In practiceexchanges have been associated with zonal prices,but there is no theoretical reason for this association.Exchanges can provide nodal prices more easilythan pools and pools were always run without nodalpricing before deregulation. Part 3 assumes that thechoice of locational pricing will be unaffected bywhether a pool or an exchange is selected. This does not mean bilateral markets should be suppressed. They should beencouraged as forward markets and allowed to exist beside the centralized DAmarket.Exchanges vs. Pools. Integrated utilities have always solved the unit-commitmentproblemcentrally, using many parameters to describe each generating unit. Incorrectunit commitment, starting the wrong set of plants in advance, can lead to twoproblems: (1) inefficiency, and (2) reduced reliability. Chapters 3-7, 3-8, and 3-9consider whether it is worth moving beyond a power exchange to a power pool.This would reproduce the old approach but with all of the parameters providedby private parties and with the pool having no direct control over the dispatchedgenerators.The disadvantages cited for an exchange are inefficiency and lack of reliabilitydue to lack of coordination. The disadvantages attributed to a pool are gamingopportunities, and biases and inefficiencies caused by side payments. The complex-ity and nontransparency of pools can also lead to design mistakes that are hard todiscover and correct.None of the efficiency or gaming concerns have received serious quantitativeassessment, and all seem overrated. Either system should be capable of performingquite well if well designed. Because the startup costs are only about 1% of retailcosts, and a simple exchange can already manage them quite efficiently, a smallincrease in bid flexibility would seem to be sufficient. In other words, a little ofthe power pool approach may be useful, but elaborate multi-part bids appear tocause more problems than they solve. While startup insurance may give the systemoperator some useful control over generator ramping, this could be obtained witha more market-oriented approach. 3-1.3 SIMPLIFIED LOCATIONAL PRICINGBecause several points concerning centralization re-quire a partial understanding of the complexity oflocational pricing, this section gives a brief overview.The properties presented here are explained more fullyin Chapters 5-3, 5-4, and 5-5.Energy prices differ by location for the simplereason that energy is cheaper to produce in some loca-tions and transportation (transmission) is limited.When a transmission line reaches its limit, it is saidto be congested, and it is this congestion that keepsenergy prices different in different locations. For thisreason locational pricing of energy is also called con-gestion pricing.Locational prices are just competitive prices, and these are unique. They aredetermined by supply and demand and have nothing to do with the architectureof the market, provided it is a competitive market. This means a purely bilateralmarket that is perfectly competitive will trade power at the same locational pricesFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-1 Introduction 207as a perfectly competitive, centralized nodal-pricing market. Of course, a bilateralmarket is likely to be less precise with its pricing, but on average it should find thefull set of competitive nodal prices.Because there is a unique set of locational prices, there is also a unique set ofcongestion prices, which will also be called transmission prices. Again, theseare determined by competition and supply and demand conditions and have nothingto do with market architecture, provided the market is perfectly competitive.If the competitive energy price at X is $20/MWh and at Y is $30/MWh, the priceof transmission from X to Y is $10/MWh. Transmission prices are always equalto the difference between the corresponding locational energy prices. If this werenot true, it would pay to buy energy at one location and ship it to the other. In thatcase arbitrage would change the energy prices until this simple relationship held.The relationship can be expressed as follows:PXY=PY !! PXThe price of transmission from X to Y equals the price of energy at Y minus theprice of energy at X. This relationship is the only one used in Part 3, but a fewrelated facts will provide a broader context.When power flows from Y to X it exactly cancels (without a trace) an equalamount of power flowing from X to Y thereby making it possible to send that muchmore power from X to Y. Thus a reverse power flow from Y to X (a counterflow)produces more transmission capacity from X to Y. As a consequence, if the priceof transmission from X to Y is positive, then the price from Y to X is the negativeof this value. This follows from the above formula, as does another consequence:The cost of transmitting power from X to Y does not depend on the path chosen.This is not surprising because, although contracts may stipulate a contract pathfor power, there is no way to influence the actual path taken. Locational pricesreflect this reality by making sure that PXZ+PZY=PXY for any intermediate pointZ.Not only is it impossible to select the path of a power flow, power takes everypossible path between two points, with more flowing on the easier routes. Theconsequence for a network with a single congested line is that every location hasa unique price. In effect there is a price for using the congested line, and everytransaction uses that line to one extent or another. Sending power from X to fiftydifferent locations will use fifty different amounts of the congested line, so therewill be fifty different transmission prices and fifty different energy prices (plusthe energy price at X). One congested line in PJ M produces 2000 differentlocational prices. A centralized market will compute these so accurately that thetrue locational differences can be seen. A bilateral market finds them imprecisely,so many observed differences will be mainly due to the haphazard nature of thebilateral process.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. Maxwell developed the mathematics of electromagnetic fields, later used to design AC motors,transformers, and power lines. He predicted the possibility of electromagnetic waves and calculated theirtheoretical velocity fromlaboratory measurements on electric and magnetic fields. At first his suggestionthat light is electromagnetic was dismissed as a not wholly tenable hypothesis.Wecan scarcely avoid theinferencethat light is thetransverseundulations of thesamemediumwhich is thecauseof electric and magnetic phenomena.James Clerk Maxwell1861This velocity is so nearly that of light, that it seems wehavestrong reasons to concludethat lightitself (including radiant heat, and other radiations if any) is an electromagnetic disturbanceintheform of waves propagated through theelectromagnetic field according to electromagneticlaws.11864Chapter 3-2The Two-Settlement SystemTHE REAL-TIME PRICE ALWAYS DIFFERS FROM THE DAY-AHEADPRICE. WHICH IS IN CONTROL? Day-ahead (DA) prices, and especially earlierprices, differ significantly from the corresponding real-time (RT) price. Thedifferences are due to misestimations made before traders know all the details ofthe RT conditions. In a competitive market the RT prices are true marginal costprices, and the forward prices are just estimates, sometimes very rough estimates.With most trade occurring in the forward markets, does this imply that only a smallproportion of generation is subject to the correct incentives? Not under a propertwo-settlement system. The purpose of the RT market is to correct the predictionerrors of the past. If the transaction costs in this market are minimized so thatprofitable trade is maximized, the RT price will be accurate and will control actualproduction. Past mistakes have financial impacts but will not cause inefficiencywhich is a purely physical phenomenon.1Contracts for differences (CFDs) insulate bilateral trades from all risks of spotprice fluctuations while allowing the inevitable inefficiencies of forward tradingto be corrected by accurate RT price signals. Both the two-settlement system andCFDs allow efficient re-contractinga standard economic solution to the problemsof decentralized forward trading. Advocates of bilateral trading have often failedto recognize this point and have opposed the very mechanisms that make decentral-February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-2 TheTwo-Settlement System 209ized trading efficient. This chapter assumes the existence of a centralized RT marketin which all generators and loads must participate.Chapter Summary 3-2: If a generator sells its output in the DA market, thetwo-settlement system lets it respond efficiently to the spot price without any riskfrom the volatility of that price. It can only profit from an unexpected spot price,and never suffer a loss. If a generator sells its power to a load in a bilateral contractmonths in advance, a CFD will let them profit efficiently from an unexpected spotprice. If they trade over lines that may be congested, purchasing an FTR (financialtransmission right) will provide the same guarantee with respect to transmissionprices. In this way forward trades that prove inefficient in real time because ofunexpected circumstances can be corrected without risk to the traders.Section 1: The Two-Settlement System. If the system operator runs a DAand an RT market, generators should be paid for power sold in the DA market atthe DA price, regardless of whether or not they produce the power. In addition,any RT deviation from the quantity sold a day ahead should be paid for at the RTprice.A CFD requires the load to pay the generator the difference between the contractprice and the spot price whether it is positive or negative. This allows either partyto deviate profitably from the contract, when the opportunity arises, withoutaffecting the other. If the spot price differs at the two locations, this hedge is notcomplete.Section 2: Ex-Post Prices: The Traders Complaint. Spot prices that differby location impose transmission costs on traders. These cannot be avoided by theuse of CFDs, and they make trade risky. Some markets in transmission rights existbut are generally limited and illiquid. Design of such markets is continuing. Afinancial transmission right (FTR) from generator to load can perfectly hedge abilateral trade that faces congestion charges. Since trade is always allowed in theRT market, an FTR is as good a guarantee as a physical right.3-2.1 THE TWO-SETTLEMENT SYSTEMIf a supplier sells most or all of its power in the forward markets, the RT price mayappear to have little chance of affecting the production decisions of suppliers. Ina properly implemented two-settlement system the opposite is true. In real time,the supplier will behave as if it were selling its entire output in the RT market, eventhough, in the forward market, it acts as if that were its final sale.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.210 PART 3 Market ArchitectureSeparation of Real-Time from Forward TransactionsSay a supplier sells Q1 to the system operator in the DA market for a price of P1.If this amount of power is delivered to the RT market, the settlement in the DAmarket will hold without modification. But what if none is delivered, or more thanQ1 is delivered? In either case the DA settlement should still hold, but there shouldbe an additional settlement in the RT market. If no power is delivered to the RTmarket, the supplier is treated as if it had delivered the amount promised in the DAmarket, Q1, but purchased that amount from the RT market to cover its promiseddelivery. Consequently the supplier is still paid P1 for Q1 but is also charged P0,the RT price, for the purchase of Q1. In general, if a supplier sells Q1 in the DAmarket and then delivers Q0 to the RT market, it will be paid:Supplier is paid: Q1P1+(Q0!! Q1) P0(3-2.1)This is called a two-settlement system. If a customer contracts for Q1 and thentakes only Q0 in real time, it is charged exactly the amount that its supplier is paid.

Result 3-2.1 A Two-Settlement System Preserves Real-Time IncentivesWhen the RT market is settled by pricing deviations from forward contracts at theRT price, suppliers and customers each have the same performance incentives inreal time as if they had traded all of their power in the RT market.The incentives of this settlement rule are revealed by rearranging the terms asfollows:Supplier is paid: Q1(P1!! P0) + Q0P0(3-2.2)When real time arrives, P1 and Q1 have been determined in the day-ahead (DA)market. Assuming the market is competitive, suppliers will also take P0 as given,so by real time, the entire first term will be viewed as a sunk cost or an assuredrevenue. This leaves the second term as the only one that can provide an RTincentive for generator behavior, and this term pays the generator the RT price forevery megawatt produced. Consequently the generator will behave exactly as ifit is selling all of its product in the RT market. This can be proven by consideringthe suppliers profit, which is revenue minus cost, and the profit it would have hadif it traded only in the RT market.Table 3-2.1 Profit With and Without a Day-Ahead TradeActual Short-Run Profit: SRBF=RF + Q0P0!! Cost(Q0)Only-Real-Time Short-Run Profit: SRB0=Q0P0!! Cost(Q0)The only difference between the two is the fixed revenue, RF=Q1(P1!! P0), sothe value of Q0 that maximizes one will maximize the other.This result means that no matter what trades, Q1, have taken place in the DAmarket, or any other forward market, profit-maximizing suppliers will pursue thesame RT strategies as if no prior trades had taken place. Consequently, if the RTmarket is competitive and therefore efficient, this efficiency will not be underminedby forward contracts. Put another way, if mistakes are made in forward marketsFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-2 TheTwo-Settlement System 211they will affect revenues but not efficiency because the RT market will induce least-cost operation regardless of these mistakes. The above argument also applies toloads.Separation from Imports and ExportsIf a supplier sells and schedules Q1 for export in a forward market for a price ofP1, and delivers this much power locally to the RT market, the exporter will owenothing and be paid nothing by the local DA and RT markets. The exporter willbe paid only by the external purchaser. But what if no power is supplied or morethan Q1 is supplied? As before, the supplier will be paid (Q0!! Q1) P0 by the RTmarket, where Q0 is its RT supply. If Q0 is zero, the supplier is paid!!Q1P0, whichmeans it is charged . This charge assumes that it has purchased in the RT Q1P0market the power that it exported. Of course the transaction could be cancelled,in which case Q1 would be adjusted to zero, and the RT payment formula wouldcontinue to apply.Separation from Bilateral MarketsIf a trader has arranged to buy Q1 at price PG from a generator and sell it to a loadat price PL, how will the participation of the generator and load in the RT marketbe handled? This transaction does not make the trader a participant in the RTmarket, yet the generators and loads must participate. Say the generator injectsQ1 and the load withdraws Q1 as the contract demands. The generator will be paidP0Q1 by the RT market which is different from what was specified in the bilat-eral contract with the traders. To compensate for this, the trader must specify thatthe generator will pay the trader P0Q1 and the trader will pay the load the sameamount. This is over and above the payments specified for the original purchaseand sale of Q1 by the trader. The entire transaction works like this (Table 3-2.2):Table 3-2.2 Details of a Bilateral Trade with AdjustmentsTrade RT Market AdjustmentGenerator is paid: PGQ1 + P0Q1 !!P0Q1Load pays: PLQ1+ P0Q1 !!P0Q1Traders net income: (PL !! PG) Q1+P0Q1!! P0Q1=0The first term for both generator and load is the payment specified by the originaltrade. The second term is the result of each participating in the RT market, and thethird term is the adjustment term specified by the trader to keep the bilateral tradeseparate from the RT market. The adjustment exactly cancels the RT settlementsof both generator and load, and for the trader, the two adjustments cancel each other.Contracts for Differences. Combining the trade and the adjustment for thegenerator defines a bilateral trade of a special type called a contract for differ-ences, a CFD. The detailed trades shown above contain two of these plus the tradeswith the RT market. The following table shows the two contracts for differencesFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.212 PART 3 Market ArchitectureContracts-for-Differences Result #1used in the above bilateral trade as well as a CFD written directly between agenerator and a load.Table 3-2.3 Contracts for DifferencesTrader pays generator: (PG !! P0) Q1Load pays trader: (PL !! P0) Q1Direct CFD: Load pays generator (PC !! P0) Q1Each bilateral trade is the contract quantity times the difference between the contractprice and the RT price. If the generator contracts directly with the load, there isonly one contract price, PC, and the load pays the generator (PC !! P0) Q1.By writing the bilateral contracts, shown in Table 3-2.3, with the generator andthe load, a trader can implement the detailed bilateral contract displayed in Table3-2.2. The RT market and adjustment terms cancel, and the effect is just as if theRT market did not exist. The same is true for a trade between a generator and aload that is implemented with a CFD. These conclusions assume the trade takesplace as specified in the contract.

Result 3-2.2 A Contract for Differences Insulates Traders from Spot Price VolatilityBilateral trades implemented through contracts for differences completely insulatetraders from the market price provided (1) the traders produce and consume theamounts contracted for, and (2) the market price is the same at the generatorslocation as at the loads location.When CFDs are used, the only effect of the spot market is to provide a convenientremedy for deviations from the contract position. Such deviations only affect theparty who deviates.Remarkably, while insulating the bilateral trade from the spot market, the CFD,together with the two-settlement system, also insulates the traders use of the spotmarket from the effects of the bilateral trade. The argument used in the beginningof this section can be used again to show that both customer and supplier willbehave as if they were trading in the RT market because their incentives to deviatefrom the contract quantity are determined by the RT price. Such deviations aredesirable and can only make them better off while doing no harm to their tradingpartners. CFDs give us the best of both worlds. Traders are protected from thevolatility of spot prices, and the efficiency of the RT market is protected from theinefficiency of forward bilateral contracting.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-2 TheTwo-Settlement System 213Contracts-for-Differences Result #2Result 3-2.3 Contracts for Differences Preserve Real-Time IncentivesBilateral traders using contracts for differences feel the full incentive of RTprices. Because they could ignore this incentive, any deviation from their contractcan only be profitable.Locational Price DifferencesSo far, spot prices have been assumed equal at all locations in the market so bothgenerator and load see the same price, but this is often not the case. As a conse-quence, the CFD can be written in different ways. To analyze this situation, assumethat generator and load have signed a CFD without the benefit of a middleman.There are two ways to write the CFD:Table 3-2.4 Two Possible CFDsEffect of CFD Loads Payment to GeneratorLoad pays for transmission: (PC !! PG0) Q1Generator pays for transmission: (PC !! PL0) Q1PG0 is the spot price at the generators bus, PL0 is the spot price at the loads bus,and PC is the contract price. In both cases, the CFD specifies the payment by loadsto generators. In the first case, because the generators RT price is used, the genera-tor is insulated from locational price differences, while in the second case, loadis insulated. To see this, the full transaction, including the RT market, must be takeninto account. Consider the case in which the generators spot price is used and inwhich each player produces or consumes as specified in the contract.Table 3-2.5 Settlements with the Generation-Centric CFDCFD Spot MarketGenerator is paid: (PC !! PG0) Q1+ PG0Q1Load pays: (PC !! PG0) Q1+ PL0Q1The first term is the CFD settlement and the second is the spot market settlement.These settlements can be simplified as follows:Table 3-2.6 Algebraic Simplification to Reveal Transmission ChargeTrade Transmission ChargeGenerator is paid: PCQ1 0Load pays: PCQ1+(PL0!! PG0) Q1Both will pay or receive the contract price, but the load must also pay the locationalprice difference times the quantity traded. Typically the spot price will be higherat the loads location, so this charge will be positive. The charge is termed acongestion charge or a transmission charge, and it arises from the scarcity ofFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.214 PART 3 Market Architecture2. This ignores the charge for losses, which is almost never above 10% and is far more predictable.3. These ex-post prices are not necessarily those that result fromthe systemof ex-post pricingdiscussed in the preface. True ex-post pricing is said to use a quantity optimization procedure that hasnot been publically specified but is rumored to be central to the PJ M and NYISO pools.4. If they trade against the prevailing flow, they create a counterflow and their consumption oftransmission service is negative, but they have still taken a position in the transmission market.transmission. It is like a transportation or delivery charge but is usually morevolatile.Congestion charges are covered in Part 5, but for present purposes it is onlynecessary to understand that they are based entirely on scarcity.2 They are typicallyzero because there is plenty of transmission capacity most of the time. When it isscarce, competition for transmission can send the price quite high. To some extentthese prices are predictable, but they contain a significant random component thatcan be problematic for traders (see Section 3-1.3).The uncertainty in the congestion price (PL0!! PG0) can be hedged by buyingenergy forwards in the two locations or by buying transmission rights between thetwo locations. If the CFD is arranged so that the load pays the congestion charge,the load may want to buy a hedge. If the CFD is set up the other way, the generatormay want to buy it. If the trade is arranged by a trader, the trader will probablyaccept the transmission charge and may want to hedge it.3-2.2 EX-POST PRICES: THE TRADERS COMPLAINT3Power traders can write CFDs and thereby completely insulate themselves fromthe spot price (and the DA price). But it is much more difficult for them to insulatethemselves from locational price differences, that is, transmission prices. If theyhave used a CFD to execute their bilateral trade and they trade as planned, the spotprice, no matter how high, will have no effect. Without a transmission right, thespot transmission price must be paid in full. Why is it so easy to insulate a bilateral trade from the spot energy price andso difficult to insulate it from the spot transmission price? A buyer and seller,considered as a unit, are unaffected by the energy price because together their netposition is zero. As a unit, however, they always take a net position in the transmis-sion market; they consume transmission from generator to load.4 Because they takea nonzero net position in the transmission market, they are affected by the priceof transmission.The complaint of traders is that the transmission price is ex-postit isestablished after they commit to a trade instead of being posted ahead of time. Theywould prefer to check the price of transmission, arrange a trade based on that price,then call up the transmission provider and purchase the desired quantity at the pricethey were quoted. United Parcel Service works this way, and their prices have twoconvenient features. First, they are posted in advance, and second, they are goodno matter how many packages are shipped. Real-time transmission prices haveneither feature. Access charges, used to cover the fixed costs of transmission, dohave these features, but they are not the focus of the traders complaint whichFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-2 TheTwo-Settlement System 215concerns only congestion charges. Two approaches to resolving this problem needconsideration: can (1) RT price setting or (2) forward markets for transmission beimproved?Better Real-time Price Setting?The system operator could post the RT congestion prices in advance. Becausecongestion prices fluctuate somewhat predictably, this would be a time-of-usetransmission charge. The bulk of bilateral trading takes place months in advance,and these charges would need to be set annually, or preferably even further inadvance. But congestion prices, as observed in systems that compute them continu-ously, have only a small component of predictability. They are susceptible toweather, generation outages, transmission outages, and other factors. When thetime-of-use price proved to be too high, valuable transmission would go unused.At other times, demand for transmission would outstrip supply, and traders wouldfind none available at the posted price. Curtailments would occur in real time, anoutcome that would be very inefficient and extremely unpopular with traders.To be of any use, time-of-use pricing must be coupled with a reservation system.FERCs pro-forma tariff provides such a system although it is based on contractpaths rather than on actual power flows and thus conflicts with the laws of physics.With a systemof interconnection-wide coordination, such as NERC is now devising,a consistent reservation system would be possible. This would avoid most RTcurtailment, but traders would still find that the posted price would not guaranteeavailability of reservations. Without a real market for transmission rights, nonpricerationing would fail to select the highest-value users and lead to an inefficientdispatch. At other times, trades would be curtailed unnecessarily.Currently, no estimate of the inefficiency of such administratively set pricesis available. The benefits of such a system are even more difficult to determine.Facilitating bilateral trading, especially long-term trading, is desirable, but thebenefits are hard to quantify. In any case, market-based prices is generally consid-ered preferable to regulated prices.Better Forward Markets for TransmissionA second approach to alleviating the traders complaint is to implement a forwardmarket in transmission rights. This has the same effect as the posted price andreservations, but the price is determined by the supply and demand for transmissioninstead of being administratively determined. PJM sells such rights in its DA marketas described in Chapter 3-3. Although this is a help, by the time traders see the DAprice of transmission, it is too late to take advantage of it. Because it is a roughguide to RT congestion prices, it is some help in deciding whether to sign a last-minute bilateral contract for power and take a chance on the RT transmission price.A continuous market is needed with a slowly changing price that traders can observebefore they arrange a trade. Afterwards they can purchase transmission at a priceclose to the observed price. So far, such markets have not been developed becauseof technical and practical problems, but new proposals are currently being debated.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.216 PART 3 Market Architecture5. This is the definition of a transmission congestion contract (TCC) as found in Hogan (1992). Manyvariations on this have been proposed and used.PJ M and the NYISO also sell firm point-to-point financial transmission rightsbetween any two points in their systems. Unfortunately these markets are quiteilliquid and a trader may have to wait for a quarterly auction to purchase the desiredright, although purchase in a secondary market is sometimes possible.If well constructed, financial transmission rights provide the security of physicalrights without some of the drawbacks. Consider how a financial right is used tohedge a bilateral trade in the RT market. A financial transmission right, FTR, fromG to L for Q1 MW is defined to pay5FTR from G to L for q pays: (PL0!! PG0) Q1.Using this FTR, reconsider the last bilateral trade of the previous section in whichload ended up paying a transmission charge.Assuming the load has purchased this FTR and the same generation-centricCFD is used, the settlement will be as follows (Table 3-2.7):Table 3-2.7 FTR Settlements with the Generation-Centric CFDCFD Spot Market FTRGenerator is paid: (PC !! PG0) Q1+ PG0Q1Load pays: (PC !! PG0) Q1+ PL0Q1 !!(PL0!! PG0) Q1Note that the FTR payment is included with a minus sign because load pays anegative amountit is paid this much by the FTR. This time when the settlementsare simplified, the load pays PCQ1 to the generator and neither pays a transmis-sion charge. Of course the FTR had to be purchased and that cost is not shown inthe settlement, but once it is purchased, the parties are immunized completelyagainst the RT transmission charge. By using both a CFD and the FTR they areprotected from fluctuations in the general level of spot prices and from locationaldifferences in the spot price.If the trade is made, there will be no transmission charge, but what guaranteesthat the parties will be allowed to trade when they have no physical reservation?Generally, RT locational energy markets allow traders to do as they wish, but theymust pay for their injections and withdrawals at the RT price. In this case no specialaction is needed by the parties; they simply make the trade and accept the charges.Provided their trade matches their FTR, the net charges will be covered exactly.If the RT market requires bids, then the generator submits the lowest possible bid(in PJM this would be !!$1,000/MWh), and the load submits the highest possiblebid. Unless there is some physical problem with the network (in which case noteven a physical reservation can guarantee the trade), they will be dispatched.Because they own the FTR they cannot be harmed by any price that results fromtheir extreme bids. The net result is an assurance that they will be able to completethe trade and be completely unaffected by the RT prices.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.1. The universe is governed by four forces and matter is made of their associated particles. The electronand photon are the carriers of the electromagnetic force, and the other three forces are gravity, the weakforce and the nuclear force. Maxwell discovered the mathematics of the electromagnetic force, Einsteinthe mathematics of the gravitational force, and Feynman the laws of the weak force which he unified withthe electromagnetic force.From a long view of the history of mankindseen from, say, ten thousand years fromnowtherecan belittledoubt that themost significant event of the19th century will bejudgedas Maxwell's discovery of thelaws of electrodynamics.Richard FeynmanOnescientific epoch ended and another began with James Clerk Maxwell.1Albert EinsteinChapter 3-3Day-Ahead Market DesignsCENTRAL DAY-AHEAD MARKETS CAN BE DESCRIBED AS AUCTIONS.The most obvious design sets energy prices based on simple energy-price bids. Adifferent approach turns the system operator into a transportation-service providerwho knows nothing about the price of energy but sells point-to-point transmissionservices to energy traders.1Either of these approaches presents generators with a difficult problem. Somegenerators must engage in a costly startup process (commitment) in order to produceat all. Consequently, when offering to sell power a day in advance, a generator needsto know if it will sell enough power at a price high enough to make commitmentworthwhile. Some day-ahead (DA) auctions require complex bids which describeall of a generators costs and constraints and solve this problem for the generators.If the system operator determines that a unit should commit, it ensures that all itscosts will be covered provided the unit commits and produces according to theaccepted bid. Such insurance payments are called side payments, and their effecton long-run investment decisions is considered in Sections 3-9.3 and 3-9.3.Chapter Summary 3-3: Day-ahead markets run by system operators are runas auctions. Although some trade energy, some sell transmission, and some solvethe unit-commitment problem, they all use the same philosophy for choosing whichbids to accept and for setting prices. Four archetypical markets are summarized:(1) a power exchange, (2) a transmission-rights market, (3) a power pool, and (4)PJ Ms DA market which mixes all three.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.218 PART 3 Market ArchitectureSection 1: Defining Day-Ahead Auctions. In DA auctions, bids are selectedto maximize total surplus, gross consumer surplus minus the cost of production.Locational energy prices are set equal to the marginal change in total surplus whenfree power is injected at the various locations. Transmission is priced at the marginalchange in total surplus when a counterflow is introduced on a transmission path.Section 2: Four Day-Ahead Market Designs. Each auction is specified bythree sets of conditions: bidding rules, bid acceptance rules, and settlement rules.Market 1 is a power exchange that uses one-part bids. Market 2 is a bilateraltransmission-rights market. Market 3 is a power pool which uses multipart bidsfor unit commitment. Market 4 combines the features of the other three as options.Section 3: Overview of the Day-Ahead Design Controversy. Forwardmarkets are bilateral, and real-time (RT) markets are centralized. The DA marketcan be designed either way, and this causes a great deal of controversy. Thecentralized nodal pricing approach specifies an energy market with potentiallydifferent prices at every node (bus) and specifies that the auction should solve theunit-commitment problem as well. This requires complex bids. The bilateralapproach specifies that energy trades take place between two private parties andnot between the exchange and individual private parties. To trade energy, the privateparties require the use of the transmission system, so the system operator is askedto sell transmission.3-3.1 HOW DAY-AHEAD AUCTIONS DETERMINE QUANTITY AND PRICEDay-ahead markets run by system operators take the form of either exchanges orpools and are operated as auctions. The process of selecting the winning bids isoften complicated by transmission and generation constraints which can requirethe use of enormously complex calculations and sophisticated mathematics. Themathematics is often presented as a way of explaining the auction. This is unneces-sary, frequently confusing, and often less precise than an approach that explainsthe purpose rather than the mechanics.A Simplified Description of AuctionsAll auctions solve some mathematical problem. Bids are submitted, some functionof the bids is maximized or minimized, and the solution determines which bidsare accepted. For example, say bids are submitted for the purchase of 100 tulipbulbs. Each bid states a number of bulbs and a total price. The auction problemmight be to maximize the sum of the accepted bid prices. The solution defines aset of accepted bids. There is one more stepsettlement. The winners must payor be paid and must provide or receive the goods being auctioned. Settlement isnot determined entirely by the solution to the acceptance problem but also usesFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-3 Day-Ahead Market Designs 219separate price-determination rules. In this example the rules could specify that eachaccepted bid would pay as bid and receive the number of bulbs bid for, or it mightspecify that accepted bids would pay a price per bulb equal to the lowest price perbulb of any accepted bid.

Summary An Auctions Three Stages: Bidding, Acceptance, and SettlementAn auction takes place in three stages1. Bids are submitted.2. Some bids are accepted and prices determined.3. Accepted bids are settled at the determined prices.The optimization problem that determines which bids are accepted does notautomatically determine prices. The pricing rule must be specified separately. The description of DA markets often focuses on presenting the auction problem,which bids to accept and what prices to set, in a format that is convenient forsolution using linear programming techniques. The solution technique is of littleinterest from an economic perspective, so presenting the problem in this way addslittle value and often much complexity. For example, the auction problem mightbe to minimize the total price of accepted bids of generators while purchasingenough power to supply a 1000-MW load at location X and taking into accountlosses. This problem can be presented as a linear programming problem thatapproximates power loss equations. But the necessary equations, while invaluableto the computer programmer, add relatively little to understanding the economics.Much of the complexity of electricity auctions is embodied in the constraintsplaced on bid acceptance by the physics of the system. Given a source (a generator)and a sink (a load), the path of the power flow is usually uncontrollable. Conse-quently, to avoid overloading lines, certain combinations of bids cannot be accepted.Losses pose similar restrictions on bid acceptance.Instead of specifying physical constraints in abstract mathematical detail, thefollowing four market summaries will simply name the constraints. The focus canthen shift to the bidding rules, the quantity being optimized in the auction problem,and the settlement rules. Settlement rules in particular often include overlookedinducements and penalties that are crucial to the functioning of a market. The shiftin focus to economic aspects, and the standardization of the descriptive formatallows easier and more meaningful comparisons of these archetypical designs forDA markets.Accepting Bids: Determining QuantitiesThe auction problem determines what bids are accepted, or partially accepted, andthis determines through simple accounting the quantities bought and sold. Pricesare determined by a separate set of settlement rules. Quantities determine theefficiency of a particular outcome, but prices provide the incentives that determinewhat bids are submitted and thereby help control the outcome.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.220 PART 3 Market ArchitectureThe Efficient-Auction ResultAll four auction designs considered in this chapter maximize total surplus asdefined by the bids. These designs encourage truthful bidding, and in a competitivemarket, bids will reflect true costs and benefits, and the auctions will maximizeactual total surplus.Total surplus is the sum of (net) consumer and producer surplus, butit is also the gross consumer surplus minus production costs. If a con-sumer offers to buy 100 MWh at up to $5,000/MWh, and the bid isaccepted, the gross consumer surplus is $500,000. If the market priceis $50/MWh, and the customers cost is $5,000, the net consumer surplusis $495,000. Similarly, if a generator offers to sell 100 MW at $20/MWh,its cost is presumed to be $2,000. If the market price is again $50/MWh,its producer surplus will be 100($50!! $20), or $3,000. Total surplusis $498,000. Writing this calculation more generally reveals that priceplayed no role in determining total surplus: Total surplus =Q(V !! P) +Q(P !! C) =Q(V !! C),where Q is the quantity traded, V is the customers gross surplus, C isthe producers cost, and P is the market price. If many bids are involved, P cancelsout of each trade. The problem of maximizing total surplus can be solved independ-ently of price determination.In an unconstrained system, total surplus can be maximized by turning thedemand bids into a demand curve and the supply bids into a supply curve andfinding the point of intersection. This gives both the market price and a completelist of the accepted supply and demand bids. Unfortunately transmission constraintsand constraints on generator output (e.g., ramp-rate limits) can make this selectionof bids infeasible. In this case it is necessary to try other selections until a set ofbids is found that maximizes total surplus and is feasible. This arduous processis handled by advanced mathematics and quick computers, but all that matters isfinding the set of bids that maximizes total surplus, and they can almost alwaysbe found.

Result 3-3.1 A Single-Price Day-Ahead Auction Is EfficientIgnoring nonconvex costs and market power, single-price DA auctions aredesigned to maximize the sum of producer and consumer surplus. Having donethis they determine locational prices that support this pattern of production andconsumption. Efficiency depends on honest bidding which results from single-price settlement and competition between bidders. Determining the Market PriceThe price determined by supply and demand is the highest of all accepted supplybids or the lowest price of an accepted demand bid. It depends on whether theintersection of the two curves occurs in the middle of a demand bid or in the middleFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-3 Day-Ahead Market Designs 2212. Total surplus should be expressed in $/h. A kilowatt, rather than a megawatt, is used to indicate thatonly a marginal change is being made. Technically one should use calculus, but this is of no practicalsignificance.Figure 3-3.1Changes in total surplusfrom the addition of1 kW of free supply willbe called the marginalsurplus.of a supply bid. When the demand curve is vertical, the intersection is always inthe middle of a supply bid, and the price is set to the supply-bid price.Whichever curve is vertical at the point of intersection has an ambiguousmarginal cost or value (see Chapter 1-6). If the demand curve has a horizontalsegment at $200 that intersects a vertical part of the supply curve that runs from$180 to $220, then the marginal cost of supply is undefined but is in-between theleft-hand marginal cost of $180 and the right-hand marginal cost of $220. (SeeChapter 1-6.) Consequently it causes no problem to say that the market price equalsboth the marginal cost of supply and the marginal value of demand.While the intersection of supply and demand is a convenient method of deter-mining price in an unconstrained market with a single price, it is cumbersome toapply to a constrained market with many prices. An alternative approach sets priceequal to marginal surplus. It determines the same price as the intersection of supplyand demand and is easier to use in a constrained system.

Definition Marginal SurplusMarginal surplus is the change in total surplus with an unit increase in costlesssupply. (Total surplus is the sum of consumer and producer surplus as well as thedifference between the supply and demand curves up to the quantity traded.) First consider the unconstrained markets shown in Figure 3-3.1. The changein total surplus when a kilowatt is added at no cost to the total supply of poweris the marginal total surplus, which because of its awkward name, will be calledsimply themarginal surplus.2 In the case depicted on the left of Figure 3-3.1, thefree unit of supply shifts the entire supply curve left while the amount producedand consumed remains unchanged. The result is a production cost savings of Ptimes 1 kW, so the marginal surplus is P. In the case depicted on the right, consump-tion is limited by the high cost of the next available generator, but if another kilowattof free supply were available, consumption would increase by 1 kW. This case ismore easily analyzed by adding the free generation out of merit order as shown.The value of consumption increases by P times 1 kW, and the cost of productionFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.222 PART 3 Market Architecture3. This is not always strictly correct. The logic of auction price determination runs fromoptimization oftrade through determination of marginal costs which then define prices. But the computer programs thatsolve these problems sometimes make use of the markets logic to find their solution.Does Price Equal Marginal Cost?Prices set by the auctions under consideration areoften called marginal-cost prices. When the demandcurve is vertical at the intersection of supply anddemand, this term is accurate. With the current lackof demand elasticity, it is almost always correct.When the demand curve intersects a verticalsupply curve, a range of marginal costs is deter-mined, as explained in Chapter 1-6. Then price is setto the marginal value of demand which is within therange of ambiguity of marginal cost.Marginal surplus is defined in both cases andnever contradicts marginal cost. Price always equalsmarginal surplus and is always equal to marginalcost or within its range of ambiguity.Figure 3-3.2Changes in total surplusfrom introducing a freekilowatt of supply at theconsumer and supplierends of a transmissionconstraint.stays constant, so total surplus increases by the same amount. In both cases marginalsurplus equals price.Next consider the constrained market diagrammed in Figure 3-3.2. All suppliersare on one side of the transmission constraint and all consumers are on the other,and the free kilowatt of supply can be introduced at either location. At the consumerend, the kilowatt increases consumption, so the marginal surplus is the marginalvalue of consumption, PD. At the supplier end, the kilowatt decreases the cost ofsupply, so the marginal surplus is the marginal cost ofsupply, PS. Because of the constraint, marginal valueand marginal cost are different, and thus the two pricesare different. Because the prices are different, thesystem operator captures part of the total surplus, butin spite of this, total surplus still equals gross consumersurplus minus the cost of production. If the supply and demand curves were smooth, theresults would be the same, but in an unconstrainedmarket, consumer value and production cost wouldjointly determine marginal surplus. If there were moreconstraints and more distinct locations, there wouldbe more prices. If demand were vertical, marginal costwould determine marginal surplus at every location.This technique for computing price handles all neces-sary complexities.Setting the market price equal to the marginal surplus is justified because it givesthe competitive price and thus induces efficient behavior. It also clears the market,which means all accepted bids will voluntarily comply with the settlement, andall rejected bids will suffer no loss given the settlement price. Trade is voluntaryat these prices.A fundamental difference between market-based and auction-based pricedetermination is that in markets marginal cost is set equal to price, while in auctions,price is set equal to marginal cost.3 (See Section 1-5.1) This causes no problemFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-3 Day-Ahead Market Designs 2234. If zones are used, the transmission constraints will represent the market less accurately, and a moreconservative representation of constraints may be required. This affects only the details of the constraintspecification and not the specification of the markets. However, zones and other complications may requiresettlement rules, not discussed here, to handle special circumstances, for example, intrazonal congestion.as long as marginal costs are correctly determined by the auction, which they arebecause the auction problem is specified as the maximization of total surplus. Thisminimizes production costs given consumption and maximizes consumer valuegiven production. This determines the same efficient pattern of production as acompetitive market and thus the same marginal costs.3-3.2 SUMMARIES OF FOUR DAY-AHEAD MARKETSThis section summarizes four archetypical DA markets, from simple to complex.Each is a locational market, and these locations may be either single buses orzones containing several buses.4Market 1: A Power Exchange. A power exchange is a centralized market thatdoes not use (make-whole) side payments. Market 1 is a classic exchange in thatit employs one-part bidsits bids consist of only a supply or demand curve. Califor-nias Power Exchange was a standard power exchange in its operation but hadimposed on it a peculiar relationship to other scheduling coordinators and to theCA ISO. Such relationships have nothing to do with the definition of an exchangemarket. Albertas power exchange uses two-part bids and serves as the completelycentralized RT spot market. Both are exchanges because they do not use generator-specific side payments and both are typical in that their bid formats are simple.

Definition Power ExchangeAn exchange market is a centralized market that does not use side payments. Atany given time and location it pays the same price to any generator selling power.It can use multiple rounds of bidding or multipart bids to determine this price andcan implement full nodal pricing. Typically, its bids are much simpler than thoseused by pools, but a centralized market using 20-part bids but not making sidepayments would still be an exchange.In some respects Market 1 is the simplest DA market. Participants do not searchfor trading partners and do not have to consider many prices in many locations.Each trader simply trades with the exchange at the traders location. The systemoperators job is simple because it ignores the unit-commitment problem. Onedifficulty, discussed in Chapter 3-9, is that competitive suppliers will not alwaysfind it most profitable to bid their marginal costs.Market 2: A Transmission-Rights Market. A transmission market is equallysimple for the system operator but requires a complex pre-market step for marketparticipants. Buyers and sellers must find each other and make provisional energytrades that are contingent on the outcome of the DA transmission market, or theymust buy transmission on speculation. As with an energy market, most transactionsFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.224 PART 3 Market Architecture5. The origins of the English pool can be traced in a memo fromLarry Ruff to Stephen Littlechild in J uneof 1989. It is available with other references at www.stoft.com. The theory of a power pool market isdescribed in Schweppe et al. (1988).can be handled in longer-term markets. The hallmark of this market is that thesystem operator does not know the price of energy, only the price of transmission.Market 3: A Power Pool. Power pool is a term used to describe an organiza-tion of regulated utilities that trade power. Such pools did not use nodal pricing,but tight pools did solve the unit-commitment problem centrally. Joskow (2000b)has said of PJ M,. . . it is not very different from the power-pool dispatch andoperating mechanisms that were used when PJM was a largetraditional power pool relying on central economic dispatchbased on marginal cost pricing principles.Pool and poolco were initially popular terms to describe this type of market,but proposals with this name were tagged as communist by the Californiabilateralists; hence those names were dropped in favor of nodal pricing andvarious related terms.5 Unfortunately these terms refer to the transmission-pricinghalf of the proposals and not to the unit-commitment part, so there is no commonterm remaining for a market that mimics an old-fashioned tight power pool. Giventhe circumstances, it seems best to continue using the old term, power pool, inanalogy to power exchange, with the understanding that in the new context ofmarket design, it refers to a market that does what a tight power pool did underregulation. In the present work, power pool will mean an auction market thatuses side payments and multipart bids to solve the unit-commitment problemcentrally; the extent of locational pricing will not be implied. As a corollary, nodalpricing will mean nodal pricing and will not imply centralized unit commitmentor side payments.

Definition Power PoolA pool is a centralized market that uses make-whole side payments to, in effect,pay different prices to different suppliers at the same time and location. Thesepayments are only made when an accepted supplier would lose money at its as-bid costs given the pool price. A pool can implement full nodal pricing. Ittypically uses multipart bids which cover all important aspects of a generatorsoperating costs and physical constraints, but a centralized market using two-partbids and making side payments is a pool.Market 4: PJMs Day-Ahead Market (2001). Market 4 is modeled on PJMscurrent market and includes all of the types of bids allowed in the previous threemarkets. This is the most complex market fromthe system operators point of view,but, like market 3, it can be quite simple for suppliers if they simply bid competi-tively. This requires only that they bid their costs.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-3 Day-Ahead Market Designs 225Table 3-3.1 Notation Used in Auction Market SummariesTerm or Symbol Definition PS(Q ), PD(Q ) Supply and demand bids. Supply bids must be nondecreasing.QDCompletely inelastic demand bid.PT, QT

Transmission bid.PE, QE, Simple energy bid (no supply or demand curve allowed).Q1, QT1Day-ahead accepted bid energy and transmission quantities.P1, PT1Day-ahead locational energy prices and transmission prices determined by the auction.Q0, QT0Actual RT transactions.P0, PT0Real-time locational energy and transmission prices.X, Y Two different locations. Used to define transmission bids and prices.Uplift A charge to load to cover unattributed costs, in this case startup insurance.Conventions and Notation for Describing AuctionsBidding, Bid Acceptance, and Settlement. The market summaries describemarket operations in terms of the three auction stages. First, restrictions on biddingare described that can have important consequences for the acceptance problem,and for market efficiency. For example, allowing 24 hourly bids instead of a singlebid for the day can increase market power. Second, bid acceptance and pricedetermination are lumped together because they are computed together, althoughconceptually they are distinct. Third, settlement includes penalties for noncompli-ance with commitments made in the auction. These typically involve RT marketprices and are crucial to the functioning of the market.Supply and Demand Curves. Usually supply curves are represented by eitherpiecewise linear functions (connect the dots with straight lines) or step functions.Typically they allow the bidder to specify about ten sloped lines or horizontal steps,but all that matters is that bidders can submit a fairly accurate approximation totheir actual supply and demand curves. Supply-curve bids must always benondecreasing.Locational Prices. Every supply and demand bid at the same location is paidor charged the same price. Transmission prices and quantities are each associatedwith two locations. The following summaries all assume that demand prices arethe same as supply prices and vary by location, but for political reasons, marketsmust usually charge loads a uniform price.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.226 PART 3 Market ArchitectureMarket 1: A Power ExchangeBidding Restrictions:Supply: PS(Q) 24 hourly bidsDemand: PD(Q) or QD 24 hourly bidsBid Acceptance and Price Determination:Acceptance problem: Maximize total surplus of accepted bids, {Q1}Constraints: Transmission limitsPrice determination: P1=marginal surplus at each locationSettlement Rules:Supply: Pay: Q1P1+(Q0!! Q1) P0Demand: Charge: Q1P1+(Q0!! Q1) P0Notes: P1 is the DA price appropriate to the location of the accepted bid, Q1. Q0 is thequantity actually produced or consumed, and P0 is the RT locational price.Comments:Because generators cannot bid their startup costs, it is generally believed theyneed to submit different price bids in different hours. Loads, whose usage islargely unrelated to price, must do the same. The set {Q1} represents the set ofaccepted bid quantities, one for each supplier and each demander, a differentone in every hour. Acceptances may be for partial quantities.The auction first finds the set of supply and demand bids which, ifaccepted, would maximize total surplus to all market participants. Then marketprice is determined at each location by the marginal surplus of additionalsupply. This can be computed by making another kilowatt-hour available at nocost, recomputing the optimal dispatch and finding the increase in totalsurplus. That value is the price per kilowatt-hour assigned to that location. Theincrease in value can come from either more consumption or from reducedproduction costs. A kilowatt-hour is used to mimic a marginal change.A DA market is a forward market, and the forward price holds if suppliersdeliver and customers take delivery of the DA quantity. Participants may notmake or take delivery of the exact quantities accepted, so strategy in the DAauction depends on the penalty for not fulfilling the DA contracts. The NYISO,for instance, confiscates the RT payments specified when Q0!! Q1>0. February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-3 Day-Ahead Market Designs 227Market 2: A Transmission-Rights Market (the bilateral approach)Bidding Restrictions:Demand: QT

fromX to Y =the marginal surplus of a 1-kW increase inthe transmission limit fromX to YSettlement Rules:Demand: Charge: QT1PT1+(QT0 !! QT1) PT0Notes: PT1 is the DA price fromX to Y. QT0 is the quantity actually produced or consumed, andPT0 is the RT price fromX to Y.Comments:PT1 is a price for transmission, not energy. If there are 10 locations there will be 90pairs of locations and consequently 90 transmission prices. These can be computedby subtracting pairs of energy prices. Adding the same constant to the energyprices leaves the differences and thus the transmission prices unchanged.Consequently the ten energy prices cannot be computed fromthe 90 transmissionprices. The total surplus fromthe transmission sold in the auction is the sumof theaccepted quantities times the respective bid prices. Bid acceptance is required tomaximize total surplus. The price of transmission is set to the marginal surplus ofincreasing transmission capability on the path in question. If the path is notconstrained the price is zero.The price of transmission, PT, is the marginal surplus of increasing thetransmission limit fromX to Y. This limit may be complicated, but an additionalfree kilowatt injected at Y and withdrawn at X is always equivalent to raising thatlimit by 1 kW. Allowing fixed-quantity bids complicates the auction problemdramatically, soit may be best not to allow them. If a partially accepted bid cannot be used, it couldbe sold, or it could be returned to the systemoperator for resale in the RT market.In this case the purchaser would earn QT1PT0 fromthe RT market. On average,arbitrage between the day ahead and RT markets should keep PT0 close to PT0.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.228 PART 3 Market ArchitectureMarket 3: A Power PoolBidding Restrictions:Supply: PS(Q), startup cost, ramp-rate limit, etc. One bid per dayDemand: PD(Q) or QD 24 hourly bidsBid Acceptance and Price Determination:Acceptance problem: Maximize total surplus of accepted bids, {Q1}Constraints: Transmission limits, ramp-rate limits, etc.Price determination: P1=marginal surplus at each location(Computed with accepted generators committed)Settlement Rules:Supply: Pay: Q1P1+(Q0!! Q1) P0Pay: Make-whole side payments for generators withaccepted bids.Demand: Charge: Q1P1+(Q0!! Q1) P0+ upliftNotes: P1 is the DA price appropriate to the location of the accepted bid, Q1. Q0 is thequantity actually produced or consumed, and P0 is the RT locational price.Comments:In PJ M, startup insurance is provided to generators who are scheduled to startup in the DA market and who do start up and follow PJ Ms dispatch.Following dispatch amounts to starting up when directed to and keepingoutput, Q, within 10% of the value that would make PS(Q) equal the RT price.Startup insurance pays for the difference between as-bid costs and thesuppliers revenue from DA and RT operations. As-bid costs include energycosts, startup costs, and no-load costs.Most generators that start up do not receive insurance payments as theymake enough short-run profits. The total cost of this insurance is less than 1%of the cost of wholesale power. Uplift includes the cost of startup insurancein this simplified market and several other charges in real markets.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-3 Day-Ahead Market Designs 229Market 4: PJMs Day-Ahead Market (2001)*Bidding Restrictions:Supply (w/UC): PS(Q), startup cost, ramp-rate limit, etc. One bid per dayDemand: PD(Q) or QD. 24 hourly bidsTransmission: QT

fromX to Y =(P1 at Y) !! (P1 at X)Settlement Rules:Energy supply: Pay: Q1P1+(Q0!! Q1) P0 +Make-whole side payments for generators withaccepted bidsEnergy demand: Charge: Q1P1+(Q0!! Q1) P0+ upliftTransmission demand: Charge: QT1PT1+(QT0 !! QT1) PT0Notes: See previous notes.Comments:Ramp-rate limit is meant as a proxy for this and various other constraints on theoperation of generators, such as minimum down time. Startup cost serves as aproxy for other costs that are not captured in the supply function PS(Q), such asno-load cost.The pure energy bids, also called virtual bids because they can be madewithout owning generation or load, are more restricted in format than the energybids made by actual load and generation.* This description is still quite simplified as it leaves out PJ Ms daily capacitymarket, various other markets, and near-markets for ancillary services and theaccompanying uplift charges.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.230 PART 3 Market Architecture6. In May 2001 the CA ISO proposed a multi-day centralized unit-commitment pool with the claimthatit intends to adopt nodal pricing as soon as practical. This was rejected by FERC. In J anuary 2002, the CAISO is again contemplating nodal pricing with centralized unit commitment.3-3.3 OVERVIEW OF THE DAY-AHEAD DESIGN CONTROVERSYThe central debate in power market design continues to be between the advocatesof centralized nodal pricing and uncoordinated bilateral trading. It is generallyagreed that RT operation should be centralized and the forward markets beyonda week should be bilateral and decentralized. At some point, as real time ap-proaches, the market structure needs to switch from uncoordinated to coordinated,and at the last second the market is almost completely replaced by the commandand control of engineers and automatic protective circuitry.The controversy focuses most intensely on the DA market with one extremeclaiming it should be highly centralized and the other claiming it should be com-pletely uncoordinated. Two compromise approaches received little attention untilrecently. The market can be semicoordinated, or it can contain all possibilities andallow the participants choose to their form of participation. PJM is evolving towardthe latter. England and California have compromised by alternating between theextremes. As the English market rejects its centralized approach in favor of mini-mum coordination, California is headed away from its uncoordinated approachtoward maximum centralization.6Nodal Pricing with Central Unit CommitmentNodal pricing refers to computing a different price at every node, or bus, of thenetwork. This system computes hundreds or thousands of different prices whenone or more of the systems lines is congested (meaning they are fully used, andit would be beneficial if they could carry more power). The point is not the manyprices as there would be as many in a competitive bilateral market. The point isthese prices are computed by an auctioneer. The centralized-nodal view encompasses a separate and unrelated tenant. Itadvocates a centralized solution to the unit-commitment problem. More recentlythis has been advocated as an option instead of a requirement. Centralized unitcommitment, but not nodal pricing, requires complex bids that describe in detailthe costs and limits of generators. In a power exchange, even one that uses nodalpricing, the auctioneer has no detailed information about generators and makesno attempt to solve this problem. The four summarized markets allow comparisonof the unit commitment part of this view but not its nodal pricing component.The Bilateral ApproachThe bilateral view generally admits that a centralized DA market is needed butcontends that it should not trade energy. Instead it should facilitate bilateral tradesof energy by selling transmission rights to the traders. This is generally claimedto be a simplification, and for the auctioneer it is a great simplification relative tosolving the unit-commitment problem. But it is no simpler than a power exchange,February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-3 Day-Ahead Market Designs 231and it makes the job of traders far more complex. They must make energy tradeswith dozens of parties in different locations with different prices, instead of justtrading with the exchange at their local price. But the point of the bilateral approachis not to simplify life for traders; it is to minimize the role of the system operatorand to maximize the role of traders.The Role of the Four Markets in the ControversyMarket 1: A Power Exchange. The pure energy market is a semi-coordinatedmarket. It compromises by taking a middle path and is simplest in operation forboth the exchange and for traders. It prices energy nodally but ignores the unit-commitment problem. This complicates the suppliers bid strategy which mustindirectly account for startup costs and generator limitations, but the market itselfremains simple. A slight complication in power exchange bidding can help genera-tors solve the unit commitment problem.Market 2: A Transmission-Rights Market. The transmission-rights marketrepresents a pure bilateral approach. This approach maximizes the role of tradersand forces traders and generators to solve the unit-commitment problem on theirown. The job of the systemoperator is no simpler than in a power exchange becauseit must still account for all transmission constraints and arrive at what is equivalentto a full set of nodal energy prices except that their collective level is indeterminate.Only the differences between locational energy prices are known to the systemoperator.Market 3: A Power Pool. Generators report as many details of their costs andlimitations as the auctioneers computer program can handle. The auctioneer thencomputes which generators should be started ahead of time. It finds the optimalsolution, assuming that the bid data and demand forecasts are correct. Because theseprograms do not find market clearing prices, and the prices they do find are toolow to induce a few of the needed generators to start up; these generators mustreceive side payments. Once these are guaranteed, the energy prices clear themarket.Market 4: PJMs DA Market (2001). PJMs market combines all the bid typesfound in the previous three markets. Together all of these bids determine one setof energy prices, and the differences between them determine the transmissionprices. Current practice is for almost all generators in PJM to use the unit-commit-ment bids for bilateral traders within PJ M to use the pure energy bids, and forbilateral traders who want to send power through PJM to use the transmission bids.One argument for this approach is that generators should be allowed to let thesystem operator solve their unit-commitment problem if that is their preference,but this does not answer the more important question of whether the systemoperatorshould offer startup insurance to generators.It should not be concluded that the use of various types of bids in PJ M indicatea clear endorsement of one or another type of DA market by any of the marketparticipants. Besides the basic rules, there are still many hard-to-quantify pressuresthat influence the choices of market participants. Nonetheless, this experiment maysomeday provide a useful comparison of the various approaches.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Electric energy thus is themost useful form of energyand at thesametimeit is the mostuseless. [It] is never used as such . . . [but] is theintermediary.Charles Proteus SteinmetzHarpersJanuary 1922Chapter 3-4Ancillary ServicesPOWER IS THE PRIMARY SERVICE, BUT SIX ANCILLARY SERVICES ARENEEDED TO ENSURE RELIABLE, HIGH-QUALITY POWER, EFFICIENTLYPRODUCED. Usually ancillary services are defined by how they are provided ratherthan by the service rendered. This results in a plethora of services and little insightinto their relationship to market design. Defining services by the benefit theyprovide and defining thembroadly produces a short but comprehensive list. Servicesdirected at long-term investment are not counted as ancillary to real-time (RT)power delivery. The six listed services require planning by the system operator,but economic dispatch is jointly provided by the system operator and the market.How that task is shared should be the subject of intense debate. Chapter Summary 3-4: Of the six ancillary services, the system operator orits agent must directly provide transmission security and trade enforcement, andto some extent economic dispatch. The other services, balancing, voltage stability,and black-start capability can be purchased from a competitive market, but thesystem operator must demand and pay for these services.Section 1: The List of Ancillary Services. Services are defined by the benefitthey provide to the market and its participants, not by their method of provision.An accurate frequency is required by some motors and particularly by large genera-tors. Many appliances need a fairly accurate voltage, and together these two servicesdefine the provision of power from the customers perspective. Transmissionsecurity and occasionally black-start capability are indirect services needed by themarket to provide the first two. Economic dispatch can include the solution of theunit commitment problem and often includes efficiently dispatching around conges-tion constraints. Trade enforcement is required to provide property rights essentialfor bilateral trading.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-4 Ancillary Services 2331. As reported in Order 888, when FERC (1996a) asked for help in defining ancillary services it receivedover a dozen different lists. One list had 38 ancillary services just for transmission. NERC presented a listof 12, though it adopted FERCs final list of six in its Glossary of Terms (NERC 1996). These six arecovered by, but do not directly correspond to, the six listed in this chapter.Section 2: Balancing and Frequency Stability. Frequency is determinedby the supplydemand balance. Frequency stability cannot be provided by individualsystem operators, but each is required to balance the real power flows in its controlarea taking into account a frequency correction. When every system provides thisbalancing service, they collectively provide frequency stability.Section 3: Voltage Stability. Voltage support is provided passively by capaci-tor banks and actively by generators. Provision is by the supply of reactive powerwhich is difficult to transmit. This makes it difficult to purchase under competitiveconditions, but long-term contracts that permit competition through entry shouldbe helpful.Section 4: Transmission Security. Transmission security can be providedinitially through the control of transmission rights or the operation of a day-ahead(DA) energy market with locational prices. In real time, a locational balancingmarket should be used.Section 5: Economic Dispatch. The system operator must assist in the provi-sion of this service by conducting a balancing market and may assist by conductinga DA power exchange or by providing almost the entire service through a powerpool.Section 6: Trade Enforcement. Once power is injected into the grid it cannotbe tracked, so ownership is lost. This makes bilateral trading impossible unlessa substitute property right is defined and enforced by the system operator, or inthe case of inter-control-area trades, by a higher authority. This property-rightsystem requires the metering of all traders, the recording of all trades, and somepower of enforcement to deter or compensate for discrepancies between registeredtrades and actual power flows.3-4.1 THE LIST OF ANCILLARY SERVICESThere are many lists of ancillary services which differ mainly in how they split andcombine the categories of service.1 The present list combines services wheneverthey differ only by speed of delivery or method of provision. The purpose is to makethe shortest possible comprehensive list that does not combine grossly dissimilarservices.The list is organized very roughly by time scale, starting with real-powerbalancing, which is of constant concern and sometimes must be provided on theFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.234 PART 3 Market Architecture2. The issue of power quality, which includes wave shape and occasional voltage spikes, will be ignored.3. Too much traffic at one time does not damage a highway, and too many phone calls will not hurt thephone wires.shortest possible time-scale, and ending with the black-start service which is seldomused.Ancillary services are those traditionally provided by the system operator insupport of the basic service of generating real power and injecting it into the grid.Much more is needed to ensure that the supply of delivered power is reliable andof high quality. Some of these services are indirect, but all ancillary services areconcerned with the dispatch, trade, and delivery of power. Looking after investmentin generation (discussed in Part 2) and transmission, while they may involve thesystem operator, are not considered ancillary services. Because the role of thesystem operator is at the heart of most architectural controversies, understandingthe ancillary services is crucial to evaluating any proposed market designs.Defining the Ancillary ServicesThis section defines the ancillary services not by how they are provided but by thebenefits they provide. The following sections describe the provision of theseservices.Frequency and Voltage. The two fundamental characteristics of power deliveredto a customer are frequency and voltage. As long as these remain correct thecustomer will have access to the needed power, and it will have the requiredcharacteristics.2 Whenever a customer encounters trouble with the supply of power,either voltage or frequency will have deviated from its allowed range. In theextreme, a power outage is defined by zero voltage.Frequency, measured in Hertz (Hz), is the number of times per second thatthe voltage goes fromits maximum(positive) value to its minimum (negative) valueand back to its maximum. This is called a cycle and frequency was formerlymeasured in cycles per second (cps). (When power is used, the frequency of thecurrent flow is the same as that of voltage, and its alternating direction of flowexplains the term, AC, alternating current.) Frequency affects the operation ofmotors, many of which draw more power and run faster at a higher frequency.Synchronous motors, the type used in AC clocks and phonographs, run at a speeddirectly proportional to frequency. But the greatest service of a stable frequencyis provided to large generatorsbasically synchronous motors operated with areverse purposewhich suffer less stress when run at a constant speed.A 10% increase in voltage will cut the life of an incandescent light bulb approxi-mately in half. Voltage is electrical pressure, and the more pressure the moreelectrical current is forced through appliances. Some are built to be insensitive tovoltage so they can be used both on 110 volt AC in North America and 220 voltAC in Europe. Low voltage can cause appliances to underperform and, oddly, canburn out some motors.Transmission Security. Compared with other networks, the transmission systemis quite fragile.3 Overuse can cause lines to overheat which can cause them to sagFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-4 Ancillary Services 235permanently or even to melt. It can also cause complex electrical problems thatinterfere with power flow. Because of such problems, most high-voltage powerlines have automatic protective circuitry that can take them out of service almostinstantly for their own protection. But protecting one line can endanger anotherand can cut off service to customers. The ancillary service of transmission securitykeeps the grid operating.In other lists of ancillary services, this service is buried within the schedulingand dispatch services. Those are the methods of providing transmission security,but they also provide other services.Voltage support is needed both as a direct customer service and to providetransmission security. This complicates its classification, but within the presentclassification of ancillary services, reactive power supply is viewed as helping toprovide two distinct services: voltage stability for customers, and transmissionsecurity. (In the case of voltage support, the method of provision is as useful amethod of classification as the benefit of the service, but consistency dictatesclassification by benefit.)Economic Dispatch. Economic dispatch refers to using the right generators inthe right amounts at the right times in order to minimize the total cost of production.Like transmission security, this service is provided by what are elsewherereferred to as scheduling and dispatch services. From an economic viewpoint,economic dispatch and transmission security are only minimally related. Economicdispatch often has nothing to do with power lines as no line limits are binding, whiletransmission security has nothing to do with the marginal cost of generators. Rollingboth into scheduling and dispatch makes some sense in a regulated world but isof little help when designing a market.Trading Enforcement. Trading enforcement is an expanded version of part (b)of NERCs sixth ancillary service (NERC, 1996) which is its interpretation of theFERCs first ancillary service required by Order 888 (FERC, 1996a):Scheduling, System Control, and Dispatch Service Providesfor a) scheduling, b) confirming and implementing an inter-change schedule with other Control Areas, including intermedi-ary Control Areas providing transmission service, and c) ensur-ing operational security during the interchange transaction.[Emphasis added]An expansion of this definition is required because trade is no longer just betweencontrol areas but also between private parties within a control area.Although this service also requires scheduling, its purpose is different fromeither economic dispatch or the provision of transmission security. This is anaccounting and enforcement service. Power trades are inherently insecure as originand ownership cannot be identified once power has entered the grid. Tradingrequires property rights which become problematic when ownership cannot beestablished. As a substitute for ownership identification, all injections and withdraw-als from the grid are metered and recorded by system operators. They also recordall trades. By matching trades with physical inputs and outputs, the honesty of thetraders can be established, and deviations from recorded trading intentions can beFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.236 PART 3 Market ArchitectureAncillary Services1. Real-power balancing (frequency stability)2. Voltage stability (for customers)3. Transmission security4. Economic dispatch5. Financial trade enforcement6. Black startdealt with appropriately. Trading enforcement comprises three steps: (1) recordingof trades, (2) metering of power flows between all traders and the common grid,and (3) settling accounts with traders who deviate.Note that this is not physical enforcement of RT bilateral trading whose absenceconstitutes the second demand-side flaw (see Section 1-1.5). This enforcementoccurs much later, but if it were implemented with extremely high penalties (notrecommended) it would have almost the same effect as RT enforcement.The Black-Start Capability. In the worst system failure, either a large part ofor an entire interconnection could be shut down. Unfortunately most generatorsmust be plugged in to get started; they require power from the grid in order tostart producing power. To start the grid, generators possessing black-start capabilityare needed. Starting a power grid requires the final ancillary service, the black-startservice. Overview of the List of Services. This completesthe list of basic tasks that must be carried out in wholeor in part by the system operator (or its agents) tosupport the basic service of RT power production.Frequency and voltage stability are the only two ser-vices provided directly to customers. Transmissionsecurity (and on rare occasions the black-start service)are provided to the wholesale market to aid in fre-quency and voltage stability. They are named sepa-rately because their role is indirect. Economic dispatch is a service provided togenerators, not to end users. Most services must be paid forthis one simplyreduces the price consumers pay for power. Trade enforcement is a service tobilateral traders. Without it bilateral trade would be impossible.3-4.2 REAL-POWER BALANCING AND FREQUENCY STABILITYFrequency stability and power balancing are two sides of the same service. Theend-use service is a stable, accurate frequency, but no system operator can providethat because it is mainly controlled by the other systems in the interconnection.Instead all system operators are required to balance their power inflows andoutflows according to NERCs ACE formula. When all system operators providethis balancing service to the interconnection, the result is a stable and accuratefrequency. The actual service provided by the system operator is balancing, butthe service provided to customers as a result of collective balancing efforts isfrequency stability. Real power is ordinary electrical power, but it is given itsfull name here to distinguish it from reactive power which is used to providethe voltage stability service.Balancing is provided by a number of different methods which are normallyclassified as separate ancillary services. Four of the six ancillary services listedby NERC and FERC fall into this category:February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-4 Ancillary Services 2374. The supply-demand balance for a given control area within the interconnection is defined by ACE,which measures a combination of frequency and inadvertent interchange (see Section 1-4.3). Thisancillary service is more properly defined as controlling ACE, but this translates into balancing supply anddemand locally and results in controlling frequency globally. 1. Regulation and Frequency Response Service2. Energy Imbalance Service3. Operating Reserve: Spinning Reserve Service4. Operating Reserve: Supplemental Reserve ServiceSome system operators further classify supplemental reserves into 10-minute, 30-minute, and replacement reserves. Also direct-control load management andinterruptible demand, as defined by NERC, would be classified as spinning reserveby some jurisdictions but might legitimately be separated by others.Frequency instability is caused by a mismatch of supply and demand, as isexplained in Section 1-4.3. When total supply in an interconnection is greater thandemand the frequency is too high, and when it is less than demand frequency istoo low.4 The comparison must be made for the entire interconnection becausefrequency is uniform throughout this region as all generators are synchronized.Within an interconnection, one market cannot have a high frequency and anothera low frequency.Supply and demand fall out of balance for three basic reasons. First, load variesin a predictable pattern throughout the day. This requires active load followingon the part of the system operator and the generators it controls. Second, there areunpredictable, constant small fluctuations in most loads and some generators, suchas wind-power generators. Third, there are generator and line outages. Corresponding to these are three basic approaches to keeping the systembalanced. Small random fluctuations are handled by a service called regulation,which utilizes generators that receive a control signal directly from the systemoperator. The process is called automatic generation control, AGC. Predictabledaily fluctuations, like the morning ramp, are handled by scheduling generationand, in an unregulated system, by the balancing market. Unexpected generationand transmission outages are handled by operating reserves of various types startingwith 10-minute spinning reserves.The Markets Role in Provision. Regulation and operating reserves aregenerally purchased by the system operator in a market that it organizes and inwhich it is the sole source of demand. Sometimes there is an attempt to havegenerators self-provide operating reserves as if they might have their own needfor such reserves. This makes little sense except as a means of preventing the systemoperator from scrutinizing the quality of the reserves provided or of capturing theservice of administering the market for operating reserves.Tracking the more predictable and larger-scale fluctuations in demand can bestbe handled by a DA market, an hour-ahead market, and an RT market. The architec-ture of this group of markets is the subject of much of Part 3. February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.238 PART 3 Market Architecture3-4.3 VOLTAGE STABILITY FOR CUSTOMERSVoltage tends to drop as power flows from generator to load, and the more powerthat flows the more the voltage tends to drop. Voltage drop also depends on thetype of load. Those involving electromagnetism, like motors and some fluorescent-light ballasts, tend to use a lot of reactive power which causes the voltage to drop.If this voltage drop is not corrected, this affects all other loads in the vicinity.Usually the voltage drop on the transmission line is corrected by a transformer thatautomatically adjusts the voltage before the power is distributed, but this processis not perfect and customer voltage fluctuates as a consequence. Voltage drop can be counteracted by the injection of reactive power (explainedin Part 5). Reactive power is quite different from real power except that its descrip-tion shares very similar mathematics. For instance, it can be supplied by capacitorswhich are entirely passive and consume no fuel. It can also be supplied by genera-tors, generally at very low cost. The cost to a generator of supplying reactive poweris mainly an opportunity cost because, while supplying reactive power consumesessentially no fuel, it does reduce the generators ability to produce real power.This relationship is nonlinear. Synchronous condensers are another source ofreactive power. These are essential generators that are run electrically. They takereal power from the grid and return reactive power.The stabilization of voltage for consumers interacts in a complex way withvoltage support for transmission security. Consequently, the customer service andthe voltage-support part of the transmission service should be considered together.However, this book will not examine either service in detail.The Markets Role in Provision. Some have proposed setting up a market inreactive power in parallel with the market in real power. The price of reactive powerwould be adjusted to clear the reactive power market.Because of the externalities associated with the consumption of reactive power,a bilateral market is out of the question. Users of reactive power would purchasefar too little. Unfortunately, reactive power is difficult to transmit. In effect it sufferslosses that are very roughly ten times greater than the losses of real power. As aresult, an RT reactive power exchange would have severe difficulties with marketpower. The system operator should, however, be able to purchase long-termcontracts for the provision of reactive power provided time is allowed for competi-tive entry. In other words, market power may be exercised over contracts sold beforecompetitors could enter. In the mean time, the system operator may need to exercisemonopsony power or regulate reactive power in order to secure it at a reasonableprice in the near term.3-4.4 TRANSMISSION SECURITYTransmission line limits are a complex matter. First there is a thermal limit. If thetotal real and reactive power on a line exceeds a certain threshold for too manyminutes the line will be permanently damaged. The most likely cause of a lineFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-4 Ancillary Services 2395. It is the square root of the sumof the squares of real and reactive power that is limited by the thermallimit, but in most cases this is quite similar to a simple limit on real power.exceeding its thermal limit is another line going out of service unexpectedly.5 Thenthe power flow on the system re-routes itself instantly, with the most flow beingtransferred to the nearest lines. In the (almost) worst case, if there are two identicalparallel lines between two regions, and these are the only lines between the regions,if one goes out of service the other receives all of its power flow. If each line couldhandle 100MW, then to protect each of them, their combined security limit wouldbe 100MW. The only benefit of having two lines instead of one would be theincreased reliability.When security limits are computed accurately, they change frequently. Forexample, suppose line L1 and L2 both have a 100 MW thermal limit and L1 woulddump 50% of its power onto line L2 if L1 were to go out of service. When L1 has100MW flowing on it, the security limit on line L2 is its 100-MW thermal limitminus the 50 MW of potential spillover from an outage on L1. The security limitof L1 is then 50 MW. If, however, L1 is carrying only 20 MW, then L2 has asecurity limit of 90 MW.Besides thermal limits there are other basic physical limits that may serve asthe basis for security limits. These are called voltage limits and stability limits. Bothare less stable than thermal limits which vary only a small amount with ambienttemperature.To provide transmission security, the system operator must first compute theselimits (and recompute some of them frequently) and then ensure that the dispatchof generation, given the existing load, is a security constrained dispatch. Thisis a set of generation output levels which, given the load, does not cause more powerto flow on any line than its security limit allows.The Markets Role in Provision. Transmission security is a service that mustbe provided by the systemoperator. It can be provided by selling transmission rightsor by controlling the acceptance of energy bids in a DA energy auction. Neithermethod is foolproof as both operate at some interval before real time. In the meantime, generators may go out of service, lines may go out, loads may increase ordecrease. Any of these can change the flow of power in such a way that a securitylimit is violated. Fortunately, in most systems, no security limit is threatened inmost hours. In PJ M, for example, no security limit is binding about 3'4 of the time.When a security limit is breached in real time, the system operator needs toinduce more generator in one location and less in another. The problem is not totalproduction; it is only a matter of where production occurs. One method of dealingwith the problem is to look for a bilateral trade that is causing power flow on thepath with the security violation and disallow that trade. The load will then haveto find another source of power. This is the current NERC approach to line-loadingrelief. It is a centralized, nonmarket approach and, as would be expected, is quiteinefficient.NERC is moving toward an RT balancing market. Essentially this amounts tolowering the RT price of power in the region where less generation is wanted andraising the RT price of power in the region where more is wanted. This is a serviceFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.240 PART 3 Market Architecturethat should be provided by using a market, but the market is only the tool used bythe system operator. The demand for security originates with the system operator,and the system operator ensures its provision. The core of the service is a highlycomplex coordination problem whose solution must be centrally provided.3-4.5 ECONOMIC DISPATCHEconomic dispatch, as defined above, is a matter of using the cheapest generation.There are two parts to this problem: (1) deciding which generators to start up, theunit-commitment problem; and (2) deciding how much to use each generator thatis running. However, most generators that are started are used at full output exceptwhen they are in transition or when one is avoiding the cost of a night-time shut-down and restart by staying on at a low output level over night.If the RT dispatch is economic, the DA market doesnt matter. Because RTsupply and demand conditions are not known precisely until real time, RT economicdispatch is quite important. Because many generators are slow and expensive tostart, the DA market plays an important role in making an efficient RT dispatchpossible.The Markets Role in Provision. There are three basic approaches to economicdispatch: (1) bilateral trading, (2) a centralized DA power exchange, and (3) acentralized DA power pool. In the first approach, suppliers and power traders solvethe entire problem. In the second, the system operator helps by running a DAexchange. The exchange provides a public price which is either used by the ex-change to select the generators that should start up or could be used by suppliersto self-select during several rounds of bidding. In the third approach, the powerpool would require generators to submit complex bids and the system operatorwould optimize the dispatch using all available bid information. That optimizationwould be used to control the actual dispatch through prices and start-up insurance.In this approach the system operator provides a full unit-commitment service. Inall approaches, the suppliers and the market price jointly determine a dispatch,which if the market is competitive, will be very nearly least cost.If the system operator relies on a competitive balancing market, the market willprovide an economic dispatch. If the system operator chooses such tools as prorata curtailment or bilateral curtailment for line-loading relief, they will interferewith economic dispatch. There is a debate over how much efficiency can beimproved by RT centralized unit commitment.3-4.6 TRADE ENFORCEMENTWhen control area A sells power across control areas B and C to control area D,how does anyone know whether A really provided the power it sold? Area D cannotmeasure As output and does not really care whether A produced the power or notbecause it can take power out of the grid in any case. The more it uses, the moreflows into its area. If the power was not produced, then frequency will decline andFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-4 Ancillary Services 241all control areas in the interconnect will be responsible for increasing supply tocorrect the problem.The origin of this problem is the fact that power cannot be tracked. Once agenerator injects power it cannot keep track of it, so it loses ownership of thatparticular piece of power. The solution to the problem is to give the supplier ofthe power a right to withdraw the same amount of power and let the supplierreassign that right at will, then enforce the rights to withdraw power. For example,when area A sells power to area D, it does so by injecting power and therebyobtaining the right to withdraw power which it then assigns to D. This solves theproblem of tracking where the power actually flows, but it requires that injectionsand withdrawals be metered and compared with the rights to withdraw power thatare granted and exercised.This is an abstract description of the principles on which the actual accountingsystem is based. In reality flows are measured between adjoining control areas,and each control area has a net scheduled interchange that is publically known.Interchange is flow on the lines connecting control areas (interties), and everyinterconnecting line is metered by both control areas. Each gets credit for outflowso they have opposite interests in terms of reporting the flow on the line. One wouldlike to err in one direction, and one would prefer to err in the other direction. Thisprevents collusion and keeps both honest.When A sells power to D, this is publically recorded as an increase in Asscheduled net interchange and a decrease in Ds scheduled net interchange. Theschedules of B and C do not change because any power that flows into them asa result of this trade also flows out. With this system of recording transactions, plusthe metering of the interties, bilateral trades between control areas can be enforced.This system creates the appropriate set of property rights.An analogous system is needed for private bilateral trades within or betweencontrol areas. For simplicity consider internal trades. If no one were watching, Acould sell power to B within the control area and then fail to produce. B would takethe power, and no one would be the wiser. The power taken would be powerproduced by some other generator somewhere in the interconnection, but there isno physical way to check on who produced the power. Again a system of tradeenforcement is needed. No matter how the details of such a system are arrangedit requires at least the following three conditions:1. All trades must be registered with the trade enforcement authority.2. All traders must have their connection to the grid metered by the authority.3. The trading authority must have the power to charge traders for discrepan-cies.

Result 3-4.1 Strictly Bilateral Power Trading Requires Centralized CoordinationWithout the central registration and measurement of all bilateral trades andpenalties for discrepancies, bilateral power trading would be impossible.Power Losses. One service which is frequently labeled an ancillary service, buthas not been mentioned so far, is the replacement of power losses. When the systemoperator balances the system, it necessarily computes a power flow from whichFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.242 PART 3 Market Architecturelosses can be approximated. Any discrepancy between actual losses and thecomputed value that is included as part of demand will be reflected in the control-areas ACE which the system operator is obliged to correct. In fact if losses arenot computed, ACE measurements could be relied on as a method of determininglosses.Thus losses are just another demand on the system and are handled throughnormal balancing. The only additional service required of the system operator isto assign the cost of losses to users. The simplest approach is to charge loads forthem in the uplift. An economic approach, discussed in Chapters 5-7 and 5-8 isto compute locational loss prices and charge generators. This calculation and itsinclusion in billing are the real services associated with losses, but these are simplypart of normal economic dispatch.The Markets Role in Provision of Trade Enforcement. Trade enforcementfor bilateral trading must be provided by the system operator. Individual tradershave no incentive to provide this service for their own trades and no power toprovide it for other trades. No other private party has the power to enforce trades.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.Economic questions involvethousands of complicated factors which contributeto a certain result.It takes a lot of brain power and a lot of scientific data to solvethesequestions. Thomas Edison1914Chapter 3-5The Day-Ahead Market in TheoryTHE DAY-AHEAD MARKET IS THE FORWARD MARKET WITH THEGREATEST PHYSICAL IMPLICATIONS. By providing financial certainty, it canremove the risk of incurring startup expenses. The more efficient the market, themore accurate the startup decisions and the lower the cost of power. Even withoutthe unit-commitment problem, reducing financial risk would reduce the cost ofcapital.As explained in Chapter 3-3, the day-ahead (DA) market can utilize one of threebasic architectures or a combination. Bilateral markets, exchanges and pools caneach provide hedging and unit commitment. The controversy over the choice ofarchitecture is driven by concerns over the shortcomings of private markets andnonprofit system operators in performing the coordination functions associatedwith unit commitment. Hedging is also an issue as pools claim to provide it morecompletely than exchanges.Some theory of market clearingwhen it is possible and when nothelps toprovide a framework for evaluating the various designs. Nonconvex productioncosts are the key to this theory, and while conceptually arcane, the focus of currentcontroversy and volumes of market rules attest to their impact on market design.Chapter Summary 3-5: Nonconvex generation costs violate an assumptionof perfect competition, but the magnitude of the resulting problems is unknown.The pool approach is designed to minimize these problems, but its pricing ignoresinvestment incentives. The bilateral approach faces formidable coordinationproblems in the DA market. It may be less efficient and provide less reliability thana centralized approach. Side-payments made by a DA pool do not increasereliability.February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.244 PART 3 Market ArchitectureSection 1: Equilibrium Without a Clearing Price. Startup and no-load costsare nonconvex and violate the assumptions of perfect competition. In particular,they often prevent the existence of a market-clearing price. Nonetheless, bilateralmarkets, exchanges, and pools all have equilibria and equilibrium prices. Bilateraland exchange prices approximate competitive prices as best they can. Consequently,they are approximately right for short-run supply and investment. Pool prices areoptimized for short-run supply but ignore investment incentives.Section 2: Difficulties with Bilateral Day-Ahead Markets. In a bilateralmarket, generators must self commit and, in doing so, they do not consider reliabil-ity. When DA load can be served at almost the same price by quick-start or slow-start generators, the market may select too many quick-start generators just bychance. Then the slow-start generators will be unavailable in real time. The uncer-tainties of the bilateral process cause decreased reliability. Bilateral markets alsohave more difficulty developing locational prices and can be expected to be lessefficient in markets with significant congestion. The magnitudes of these effectsare unknown.Section 3: Settlement, Hedging, and Reliability. Selling power in the DAmarket provides a hedge against the risks of the volatile real-time (RT) price. Forthe hedge to work, the supplier must commit its generator and be prepared toproduce according to its DA contract. Thus DA contracts provide some inducementto commit units as a way of reducing risk. If the DA contract is with a pool andtherefore includes a make-whole side payment, this leads to no increase in theincentive to commit because that payment is not contingent on RT performance.Section 4: Other Design Considerations. These include transaction costs,facilitation of market monitoring, provision of publicly known prices, and nondis-criminatory access. Penalties for avoiding the DA market should not be used inan attempt to obtain more accurate unit-commitment data.3-5.1 EQUILIBRIUM WITHOUT A CLEARING PRICEThe theory of perfect competition, explained in Parts 1 and 2, assumes that thereis a price that clears the market when suppliers take that price as given. In thiscase a competitive market is efficient, but if production costs are nonconvex, theremay be no market clearing price, and when there is none, economic theory doesnot guarantee efficiency. Startup costs and no-load costs are nonconvex, andsome constraints on generation output cause similar problems.Although these nonconvex costs cause deviations from perfect competition,the deviations may be inconsequential. The debate over the power pool approachconcerns the magnitude of the resulting inefficiency. This inefficiency can takeFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-5 TheDay-Ahead Market in Theory 2451. Scarcity rent (see Section 1-6.6) is revenue minus costs that vary with output. After startup and no-loadcosts are subtracted, short-run profits remain.three forms. Nonconvex costs can cause (1) an inefficient but reliable dispatch,(2) decreased reliability, or (3) financial risks for generators. The justificationclaimed for the complexity of the pool approach is that it minimizes these threeinefficiencies. Why There May Be No Clearing PriceA market clearing price is a single price that causes supply to equaldemand. Suppose power is needed for just two hours and exactly 100MW is needed. Suppose there are a number of competing generators,so they offer to supply at a competitive price. Their marginal cost is$20/MWh up to their capacity of 200 MW, and their startup costs are$30/MW started. Ignoring demand limitations, at a price of $35/MWha generator can earn a scarcity rent of $15/MWh for two hours on eachMW of its capacity for a total scarcity rent of $30/MW.1 This wouldexactly cover its start up cost. At a lower price it would not voluntarilyagree to sell any power. At a price of $35/MWh or more it would offerto supply its full 200 MW.Below $35/MWh supply is zero, while at or above $35 supply is 200MW or greater. There is no price at which supply equals 100 MW.Technically, there is no price at which a supplier could profitably sell 100 MWbut could not increase its profit by selling more. Thus there is no price at whichsupply equals the 100 MW level of demand. There is no market clearing price. (SeeSection 3-9.2 for another example.) The root of the problemis that production costsare not convex. Convex production costs have the property that twice as muchoutput always costs at least twice as much to produce. In this case 100 MW fortwo hours would cost $50/MWh, while 200 MW for two hours would cost$35/MWh. Twice as much is cheaper per unit, so the production cost function isnot convex.A Bilateral EquilibriumMarket clearing is often defined narrowly in the context of perfect competition,but sometimes it is defined more broadly to mean that no profitable trades remainto be made. To avoid confusion this situation will be referred to as an equilibriumbut not as market clearing. This definition will be used with bilateral markets. Inthe above example, a bilateral market could reach an equilibrium by arranging atrade in which 100 MW of power was sold for two hours at a price of $35/MWh.Having made that trade, demand would be satisfied and no further trade couldprofitably take place. In this context profitably takes account of the consumersvalue as well as the suppliers profit.Because of bargaining problems, it is not obvious that a bilateral market wouldreach this equilibrium. In a more complex and realistic market, the frictions ofbilateral trade inherent in the costly process of gathering information and arrangingFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.246 PART 3 Market Architecture2. Auction rules specify what bids are acceptable including the fact that prices must be rounded to thepenny and quantities to the MW. These rules and limitations imply the auction is a finite game (playershave a finite though large number of strategies available). In solving such games, it appears that thefiniteness of the strategy set is not required to produce a Nash equilibrium.trades could also prevent the market from reaching equilibrium, especially giventhe limited trading time of a DA market. Even if equilibrium is reached there is no guarantee that it will be efficient (leastcost) in a market with nonconvex costs. But even if inefficient, in a large market,this inefficiency may prove to be too small to matter. The problems caused bynonconvex costs in a real power market with a peak load of 10 GW and a 1 GWinterconnection to a larger outside market may be entirely negligible. This is amatter for empirical research or detailed theoretical calculations.An Exchange EquilibriumA bilateral market can reach an equilibrium by trading at more than one price, butan exchange is limited to a single price. With nonconvex costs, there may be noprice that clears an exchange market. In spite of this the exchange will always havean equilibrium. Exchanges are auctions and, as described in Chapter 3, have adefinite set of rules that determine what bids will be accepted and how they willbe settled. The Nash theorem states that such games always have at least one Nashequilibrium.2An equilibriumof an exchange market will be defined to be a Nash equilibrium,a situation in which no player could do better by bidding differently, provided otherplayers maintain their equilibrium bids. Using this definition, the Nash theoremguarantees the market will have at least one equilibrium. Examples of this are givenin Chapter 9.Although the exchanges equilibrium price cannot clear the market, it will tendto come as close as possible in the sense of minimizing the gap between competitivesupply and competitive demand. For example, the market may clear except for asingle generator that sells less than its full output while wishing it could sell it allat the market price.A Pool EquilibriumLike an exchange, the equilibrium of a power pool is defined as any Nash equilib-rium of the pool auction. Like an exchange and a bilateral market, a pool determinesan equilibrium set of quantities traded. Unlike an exchange, a pool does not deter-mine a single market price. Instead, it determines a nominal market price, the poolprice, and a set of supplier-specific side payments which, in effect, create a differentprice for each supplier. In practice many suppliers will receive no side paymentand so this group will be paid the same price, the nominal market price. But, bydesign, the pool allows every supplier to be paid a different price.The average of the individual prices in a pool approximates the price in anexchange, but the nominal pool price is lower and could be much lower. In practiceit appears to be lower by (very roughly) 3%. As an example consider a market withgenerators having marginal costs of $20.00/MWh, $20.10/MWh, $20.20/MWhFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-5 TheDay-Ahead Market in Theory 2473. Pool prices claimto send efficient signals to consumers but ignore some implications of nonconvexproduction costs. When the optimal dispatch occurs at a production level for which marginal cost is notdefined, pool prices send the wrong signal to consumers. This circumstance occurs with a significantprobability. Chapter 3-8 gives an example which proves this point.and so on. Assume they have no startup costs but have a no-load cost that averages$10/MWh when they produce at full capacity. Assume the generators are smallrelative to the market size so that the integer (lumpiness) problemis of little concern.A pool price is defined by system marginal cost which is $25/MWh if the 51stgenerator is needed. This generator would receive a side payment of $10/MWhto cover its no-load cost. An exchange would need to set a single market price of$35/MWh to induce this supplier to produce. Thus the nominal pool price can bedramatically lower than the price that comes closest to clearing the market anddramatically lower than the market price of a power exchange. The difference ismainly, but not entirely, made up by the side payments.The Efficiency Of Equilibrium PricesBilateral prices and exchange prices approximate competitive prices in the sensethat they come about as close to clearing the market as possible. Pool prices arebased on a different philosophy. They are designed to solve one problem optimallywhile ignoring two others. Competitive prices, when they exist, play three usefulroles: (1) they induce least cost supply given demand, (2) they induce efficientconsumption, and (3) they induce efficient investment in generation capacity.Bilateral markets and exchanges provide prices that approximately achieve all threeefficiencies while pool prices succeed perfectly at (1) while ignoring (2) and (3).3The demand-side efficiency of pool prices is discussed in Chapter 3-8, while long-run efficiency is discussed in Chapters 3-8 and 3-9.Notice that, in the above example, the generator with a $20/MWh marginal costwould lose money if paid only the nominal pool price of $25/MWh, so it wouldbe given a side payment of $5/MWh. Its total cost at full output, $30/MWh, wouldthen just be covered. Had this been an exchange or bilateral market, the almost-clearing price would have been $35/MWh. With regard to short-run supply, thismakes no difference since, given demand, the pool always induces an efficientdispatch. But with $5/MWh less revenue to cover fixed costs, long-run incentiveswill be quite different. A pool does not concern itself with these incentives whensetting price and its philosophy of price setting does not produce efficient long-runincentives as a side effect.Again, the real-world implication may be minimal and empirical research ordetailed theoretical analysis is needed. The more difficult question is whether themodest increase in efficiency attributed to optimizing short-run supply exceedsthe modest loss of efficiency from ignoring the long run.3-5.2 DIFFICULTIES WITH BILATERAL DAY-AHEAD MARKETSMarkets should be encouraged as long as they do not inhibit the provision ofancillary services by the system operator. These services are needed in real time,February2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.248 PART 3 Market Architecture4. This assumes that there are enough quick-start generators to substitute for most of the slow-startgenerators that have nearly the same average costs including startup costs.not a day ahead, so the DA market can be problematic only to the extent it interfereswith RT operations. Trades made in the DA market can be rearranged in real timeas neededwith one exception. If a generator has not been started and is slow tostart, it may be unavailable when needed in real time. Thus, proper unit commitmentis sometimes required for balancing and calls for special attention when evaluatingDA market designs. The ancillary service of transmission security also impingeson the design of the DA market by adding complexity to its operation.Balancing and Unit CommitmentReal power balancing mainly refers to small, but often quick, adjustments of supplyto keep it equal to demand. If demand cannot be balanced because of a shortageof supply, load must be shed. This is the most extreme result of imbalance and themost important problem that could be caused by the DA market. The possibilityof this failure is greatest in a bilateral market.Example of a Unit-Commitment Failure. Consider a bilateral market with20 identical slow-start, midload generators, each with a different owner, only 10of which are needed on a particular day. With 20 identical generators and only 10needed, competition will be stiff and expected profits will be zero, but dependingon the number that commit, actual profits will be positive or negative. Before tradingbegins, each generator knows that it has a 50/50 chance of selling its power in theDA market, but it is indifferent as to whether it does or not because in either caseits expected profit is zero.On the first round of trading, because there is no coordination in a bilateralmarket, an average of 10 generators will sell power, but because of randomness,5.8% of the time six or fewer will be committed.4 When this happens there is a goodchance that an unexpected RT event will cause a shortage and prices will be veryhigh. There is even a chance of a backout because there may not be enough quick-start generators to make up for the lack of committed slow-start generators. Normally, a bilateral market would fix this type of problem. Some customerswould realize they might be the ones demanding extra power in a tight market, orsome generators would realize they might have a forced outage and need to buyextremely expensive replacement power. But the re-contracting process also takesplace without coordination. J ust as the outcome of the initial round is partiallyrandom, so is the outcome of re-contracting.With enough time and with low-enough re-contracting costs, a bilateral marketwill reach the optimal solution. But with only a few hours of trading it may noteven learn what collective mistakes were made in the first round. The problem isnot that bilateral markets have an inefficient equilibrium; the problemis that withoutcoordination and with a very limited trading time, they have a great deal of troublefinding the equilibrium. This is especially true when the optimal set of tradesdepends on the distribution of generation technologies selected and not just on thecharacter of individual trades. As a consequence, bilateral trading in a constrictedtime frame produces results that are more random with regard to reliability thanFebruary2002. Steven Stoft, Power System Economics (IEEE/Wiley) ISBN 0-471-15040-1.CHAPTER 3-5 TheDay-Ahead Market in Theory 249does a centralized market. The optimal solution to the reliability problem is nota randomized level of commitment, so bilateral markets provide less reliability.The magnitude of the problem deserves investigation, but for the present,randomness of commitment in a bilateral market must be taken seriously. Powermarkets that rely on bilateral DA markets usually do take it seriously and providesome non-market arrangement to help ensure sufficient commitment. One mitigatingfactor is that days with serious reliability problems are usually extremely profitable,and any hint of such a problem is likely to produce ample commitment.

Result 3-5.1 A Bilateral DA Market Decreases ReliabilityBecause of information problems, a bilateral market, while getting essentially theright answer on average, will produce a more random outcome than a centralizedmarket with respect to the level generating units committed in advance. Thisrandomness reduces the efficiency of the market and its reliability. The magnitudeof this effect has not been determined.Transmission SecurityThe DA market cannot easily interfere with transmission security, but transmissionlimits complicate the DA market. If locational pricing is needed because of trans